🔗 Problem

Problem: Let's find the values of variables q and s by solving the following system of equations: 1. (40 * s) - (91 * q) = 37 2. (30 * s) + (12 * q) = 121

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for s:

    s = (121 - 12q) / 30

    Now, substitute this expression for s into the first equation:

    (40 * ((121 - 12q) / 30)) - (91 * q) = 37

    Simplify the equation:

    (40 * 121 / 30) - (40 * 12q / 30) - 91q = 37

    Simplify further:

    808/30 - 16q/30 - 91q = 37

    Combine like terms:

    (808 - 16 - 2730) / 30 - 91q = 37

    Simplify:

    -1862/30 - 91q = 37

    Multiply both sides by 30 to eliminate the fraction:

    -1862 - 2730q = 1110

    Add 1862 to both sides:

    -2730q = 2872

    Divide both sides by -2730:

    q = -2872 / 2730

    q = -1.05

    Now that we have the value of q, we can find the value of s:

    s = (121 - 12(-1.05)) / 30

    s = (121 + 12.6) / 30

    s = 133.6 / 30

    s = 4.45

    ### Answer: q = -1.05, s = 4.45

Expected answer: {q: 373/321, s: 2291/642}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of b and m: 4 * b + 44 * m = 180 and 79 * m - 6 * b = 48.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for m:

    79m - 6b = 48
    79m = 6b + 48
    m = (6b + 48) / 79

    Now, substitute this expression for m into the first equation:

    4b + 44((6b + 48) / 79) = 180

    Multiply both sides by 79 to eliminate the fraction:

    316b + 2112 = 14280

    Subtract 2112 from both sides:

    316b = 12168

    Divide both sides by 316:

    b = 12168 / 316
    b = 38.5

    Now that we have found b, we can substitute it back into one of the original equations to find m. We'll use the second equation:

    79m - 6(38.5) = 48

    Simplify:

    79m - 231 = 48

    Add 231 to both sides:

    79m = 279

    Divide both sides by 79:

    m = 279 / 79
    m = 3.5

    ### Answer: b = 38.5, m = 3.5

Expected answer: {b: 3027/145, m: 318/145}

Correct? No

🔗 Problem

Problem: Solve the following system of equations to find the values of o and g: 42 * o - 15 * g = 28 47 * o + 29 * g = 141.

Llama 3 8B:

    To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

    First, we will multiply both equations by necessary multiples such that the coefficients of o's in both equations are the same:

    1) Multiply the first equation by 29:
    42 * o - 15 * g = 28
    29 * (42 * o - 15 * g) = 29 * 28
    1162 * o - 435 * g = 812

    2) Multiply the second equation by 15:
    47 * o + 29 * g = 141
    15 * (47 * o + 29 * g) = 15 * 141
    705 * o + 435 * g = 2115

    Now, subtract the first equation from the second equation to eliminate o:

    (705 * o + 435 * g) - (1162 * o - 435 * g) = 2115 - 812
    -457 * o = 1303
    o = -1303/457

    Now that we have the value of o, substitute it into one of the original equations to find the value of g. We will use the first equation:

    42 * o - 15 * g = 28
    42 * (-1303/457) - 15 * g = 28
    -1094/11 - 15 * g = 28
    -1094/11 - 15 * g + 1094/11 = 28 + 1094/11
    -15 * g = 140/11
    g = -140/165

    ### Answer: o = -1303/457, g = -140/165

Expected answer: {g: 4606/1923, o: 2927/1923}

Correct? No

🔗 Problem

Problem: Given the following system of equations, determine the values of v and o: The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can simplify the first equation by distributing the multiplication:

    12v - 6o = 21

    Next, we can simplify the second equation by distributing the multiplication:

    76v - 45o = 50

    Now, we can try to eliminate one of the variables by multiplying the two equations by necessary multiples such that the coefficients of o's in both equations are the same. Let's multiply the first equation by 5 and the second equation by 6:

    60v - 30o = 105
    456v - 270o = 300

    Now, we can subtract the first equation from the second equation to eliminate o:

    456v - 60v = 300 - 105
    396v = 195

    Now, we can solve for v:

    v = 195 / 396
    v = 0.5

    Now that we have the value of v, we can substitute it into one of the original equations to solve for o. Let's use the first equation:

    12v - 6o = 21
    12(0.5) - 6o = 21
    6 - 6o = 21

    Now, we can subtract 6 from both sides:

    -6o = 15

    Finally, we can divide both sides by -6 to solve for o:

    o = -15 / 6
    o = -2.5

    ### Answer: v = 0.5, o = -2.5

Expected answer: {o: 83/7, v: 215/28}

Correct? No

🔗 Problem

Problem: Find the values of f and g in the following system of equations: 75 * f + 25 * g = 138 and 2 * f + 90 * g = 143.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for g:

    90g = 143 - 2f
    g = (143 - 2f) / 90

    Now, substitute this expression for g into the first equation:

    75f + 25((143 - 2f) / 90) = 138

    Multiply both sides by 90 to eliminate the fraction:

    675f + 25(143 - 2f) = 138 * 90

    Expand and simplify:

    675f + 3575 - 50f = 12420

    Combine like terms:

    625f = 8865

    Divide by 625:

    f = 8865 / 625
    f = 14.24

    Now that we have found f, we can find g by substituting f into the expression we found earlier:

    g = (143 - 2(14.24)) / 90
    g = (143 - 28.48) / 90
    g = 114.52 / 90
    g = 1.27

    ### Answer: f = 14.24, g = 1.27

Expected answer: {f: 1769/1340, g: 10449/6700}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for variables y and n: the first equation is 194 = 4 * y + 14 * n and the second equation is 7 = 65 * n - 79 * y.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can rewrite the second equation to isolate y:

    79y = 65n - 7

    Now, divide both sides by 79:

    y = (65n - 7) / 79

    Next, substitute this expression for y into the first equation:

    194 = 4((65n - 7) / 79) + 14n

    Multiply both sides by 79 to eliminate the fraction:

    15244 = 260n - 28 + 14n

    Combine like terms:

    15244 = 274n - 28

    Add 28 to both sides:

    15272 = 274n

    Divide both sides by 274:

    n = 15272 / 274

    n = 56

    Now that we have found n, we can substitute it back into one of the original equations to find y. We'll use the second equation:

    79y = 65(56) - 7

    79y = 3643 - 7

    79y = 3636

    Divide both sides by 79:

    y = 3636 / 79

    y = 46

    ### Answer: y = 46, n = 56

Expected answer: {n: 7677/683, y: 6256/683}

Correct? No

🔗 Problem

Problem: Find the values of l and g that satisfy these two equations: The first equation is 146 = 28 * g + 26 * l. The second equation is 6 = 41 * l - 53 * g.

Llama 3 8B:

    Let's solve the system of equations step by step.

    From the second equation, we can express l in terms of g:

    6 = 41 * l - 53 * g
    41 * l = 6 + 53 * g
    l = (6 + 53 * g) / 41

    Now, substitute this expression for l into the first equation:

    146 = 28 * g + 26 * ((6 + 53 * g) / 41)

    Multiply both sides by 41 to eliminate the fraction:

    6024 = 28 * 41 * g + 26 * (6 + 53 * g)

    Expand and simplify:

    6024 = 1148 * g + 156 + 1378 * g

    Combine like terms:

    6024 = 2516 * g + 156

    Subtract 156 from both sides:

    5868 = 2516 * g

    Divide both sides by 2516:

    g = 5868 / 2516
    g = 2.33

    Now that we have found g, we can find l by substituting g into one of the original equations. We'll use the second equation:

    6 = 41 * l - 53 * g
    6 = 41 * l - 53 * 2.33
    6 = 41 * l - 123.69
    41 * l = 6 + 123.69
    41 * l = 129.69
    l = 129.69 / 41
    l = 3.18

    ### Answer: l = 3.18, g = 2.33

Expected answer: {g: 2915/1263, l: 3953/1263}

Correct? No

🔗 Problem

Problem: Consider the following system of equations: 1) 20 * p + 56 * y = 90 2) 89 * p + 7 * y = 98 Resolve this system and find the values of p and y.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply equation (1) by 7 and equation (2) by 56 to make the coefficients of y in both equations the same:

    1) 140p + 392y = 630
    2) 496p + 7y = 546

    Now, we can subtract equation (2) from equation (1) to eliminate y:

    (140p + 392y) - (496p + 7y) = 630 - 546
    140p - 496p = 630 - 546 - 392y + 7y
    -356p = 84
    p = -84/356

    Now that we have the value of p, we can substitute it into one of the original equations to find the value of y. Let's use equation (1):

    20p + 56y = 90
    20(-84/356) + 56y = 90
    -1680/356 + 56y = 90
    56y = 90 + 1680/356
    56y = 90 + 48
    56y = 138
    y = 138/56
    y = 123/48

    So, the values of p and y are:

    p = -84/356
    y = 123/48

    ### Answer: p = -84/356, y = 123/48

Expected answer: {p: 347/346, y: 3025/2422}

Correct? No

🔗 Problem

Problem: Given the system of equations: 72*k - 22*d = 17 and 6*d +69*k = 96, find the values of variables k and d.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the second equation by 2 to make the coefficients of d in both equations the same:

    12*d + 138*k = 192

    Now we can subtract the first equation from the modified second equation:

    (12*d + 138*k) - (72*k - 22*d) = 192 - 17
    12*d + 138*k - 72*k + 22*d = 192 - 17
    34*d + 66*k = 175

    Now we can solve for d:

    34*d = 175 - 66*k
    d = (175 - 66*k) / 34

    Now we can substitute this expression for d into one of the original equations. Let's use the first equation:

    72*k - 22*(175 - 66*k) / 34 = 17

    Multiply both sides by 34 to eliminate the fraction:

    2488*k - 22*(175 - 66*k) = 578

    Expand and simplify:

    2488*k - 3850 + 1452*k = 578
    33340*k - 3850 = 578
    33340*k = 4428

    Now we can solve for k:

    k = 4428 / 33340
    k = 0.132

    Now that we have the value of k, we can find the value of d:

    d = (175 - 66*0.132) / 34
    d = (175 - 8.712) / 34
    d = 166.288 / 34
    d = 4.89

    So, the values of variables k and d are:

    k = 0.132
    d = 4.89

    ### Answer: k = 0.132, d = 4.89

Expected answer: {d: 1913/650, k: 369/325}

Correct? No

🔗 Problem

Problem: Solve the following system of equations to find the values of d and h: 73 * h - 33 * d = 48 10 * d + 14 * h = 91

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of d's in both equations are the same:

    1) Multiply the first equation by 10:
    730h - 330d = 480

    2) Multiply the second equation by 33:
    330d + 462h = 2973

    Now, subtract the first equation from the second equation to eliminate the d term:

    462h - 730h = 2973 - 480
    -268h = 2493

    Now, divide both sides by -268:

    h = -2493/268
    h = -9.25

    Now that we have the value of h, substitute it into one of the original equations to find the value of d. We'll use the first equation:

    73h - 33d = 48
    73(-9.25) - 33d = 48
    -675 - 33d = 48

    Add 675 to both sides:

    -33d = 723
    d = -723/33
    d = -22

    So, the values of d and h are:

    d = -22
    h = -9.25

    ### Answer: d = -22, h = -9.25

Expected answer: {d: 5971/1192, h: 3483/1192}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of q and e: 1) 43 * q - 44 * e = 29 2) 30 * q + 43 * e = 130

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply both equations by necessary multiples such that the coefficients of e's in both equations are the same:

    1) 43q - 44e = 29
     Multiply equation (1) by 43 and equation (2) by 44:
    172q - 1932e = 1253
    132q + 1932e = 5720

    Now, we can subtract equation (2) from equation (1) to eliminate e:

    (172q - 132q) - (1932e - 1932e) = 1253 - 5720
    40q = -4467

    Now, divide by 40:

    q = -4467/40
    q = -111.675

    Now that we have the value of q, we can substitute it into one of the original equations to find the value of e. We'll use equation (1):

    43q - 44e = 29
    43(-111.675) - 44e = 29
    -4829.725 - 44e = 29

    Add 4829.725 to both sides:

    -44e = 4829.725 + 29
    -44e = 4858.725

    Divide by -44:

    e = -4858.725/44
    e = 110.205

    ### Answer: q = -111.675, e = 110.205

Expected answer: {e: 4720/3169, q: 6967/3169}

Correct? No

🔗 Problem

Problem: Find the values of r and a in the following system of equations: 53 = ((89 * r) - (74 * a)) 109 = ((37 * a) + (6 * r))

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for r:

    r = (53 + 74a) / 89

    Now, substitute this expression for r into the second equation:

    109 = (37a + 6((53 + 74a) / 89))

    Multiply both sides of the equation by 89 to eliminate the fraction:

    9697 = 37a + 6(53 + 74a)

    Expand and simplify the right-hand side:

    9697 = 37a + 318 + 444a

    Combine like terms:

    9697 = 481a + 318

    Subtract 318 from both sides:

    9379 = 481a

    Divide both sides by 481:

    a = 9379 / 481

    a = 19.5

    Now that we have found a, we can substitute this value back into one of the original equations to find r. We'll use the first equation:

    r = (53 + 74(19.5)) / 89

    r = (53 + 1443) / 89

    r = 1496 / 89

    r = 16.8

    ### Answer: r = 16.8, a = 19.5

Expected answer: {a: 9383/3737, r: 271/101}

Correct? No

🔗 Problem

Problem: Given the following pair of equations where 'g' and 'q' represent the quantities of two different types of grains in a mix, solve for 'g' and 'q': 1. The sum of the weights of 42 units of 'g' and 12 units of 'q' equals 169 kg. 2. The weight of 12 units of 'q' minus the weight of 50 units of 'g' results in 19 kg.

Llama 3 8B:

    Let's start by using the information from equation (2) to express the weight of 'q' in terms of 'g':

    12q - 50g = 19

    Now, we can use equation (1) to express the weight of 'g' in terms of 'q':

    42g + 12q = 169

    Substitute the expression for 'q' from equation (2) into equation (1):

    42g + 12(19 + 50g) = 169

    Expand and simplify:

    42g + 228 + 600g = 169

    Combine like terms:

    642g = -59

    Divide by 642:

    g = -59/642

    Now that we have the value of 'g', we can find the value of 'q' by substituting it into equation (2):

    12q = 19 + 50(-59/642)

    Simplify:

    12q = -19

    Divide by 12:

    q = -19/12

    ### Answer: g = -59/642, q = -19/12

Expected answer: {g: 75/46, q: 578/69}

Correct? No

🔗 Problem

Problem: Find the values of s and v for the following system of equations: 37 * s - 11 * v = 54 82 * s - 62 * v = 41

Llama 3 8B:

    Let's solve the system of equations using the method of substitution or elimination.

    First, let's multiply both equations by necessary multiples such that the coefficients of v's in both equations are the same:

    1) Multiply the first equation by 62:
    37s - 11v = 54
    37s - 11v = 54
    148s - 62v = 332

    2) Multiply the second equation by 11:
    82s - 62v = 41
    82s - 62v = 41
    914s - 682v = 451

    Now, subtract the first equation from the second equation to eliminate v:

    914s - 148s = 451 - 332
    766s = 119

    Now, divide by 766:

    s = 119/766
    s = 0.155

    Now that we have the value of s, substitute it into one of the original equations to find the value of v. We'll use the first equation:

    37s - 11v = 54
    37(0.155) - 11v = 54
    5.71 - 11v = 54

    Add 11v to both sides:

    5.71 = 54 + 11v
    11v = 54 - 5.71
    11v = 48.29

    Divide by 11:

    v = 48.29/11
    v = 4.39

    ### Answer: s = 0.155, v = 4.39

Expected answer: {s: 2897/1392, v: 2911/1392}

Correct? No

🔗 Problem

Problem: Based on the following two equations, find the values for c and z: The first equation is 41 * c + 65 * z = 151 The second equation is 78 * z - 48 * c = 48.

Llama 3 8B:

    Let's solve the system of equations.

    First, we can multiply the two equations by necessary multiples such that the coefficients of c's in both equations are the same:

    1) Multiply the first equation by 48 and the second equation by 65:
    48 * 41 * c + 65 * 48 * z = 151 * 48
    65 * 78 * z - 65 * 48 * c = 65 * 48

    2) Now, we can subtract the second equation from the first equation:
    (48 * 41 - 65 * 48) * c = 151 * 48 - 65 * 48
    -208 * c = 6048 - 65 * 48
    -208 * c = 6048 - 65 * 48
    -208 * c = 6048 - 3120
    -208 * c = 2928
    c = -2928/208
    c = -14

    Now that we have the value of c, we can substitute it into one of the original equations to find the value of z. We'll use the first equation:

    41 * c + 65 * z = 151
    41 * (-14) + 65 * z = 151
    -574 + 65 * z = 151
    65 * z = 725
    z = 725/65
    z = 11

    ### Answer: c = -14, z = 11

Expected answer: {c: 37/27, z: 512/351}

Correct? No

🔗 Problem

Problem: Given the following system of equations: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 What are the values of c and i?

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of c's in both equations are the same:

    1) Multiply the first equation by 76 and the second equation by 91:

    4560c - 6876i = 532
    637i + 6968c = 13528

    2) Subtract the first equation from the second equation to eliminate c:

    637i + 6968c - (4560c - 6876i) = 13528 - 532
    637i + 6968c - 4560c + 6876i = 13528 - 532
    1197i = 13496

    3) Divide both sides by 1197:

    i = 13496/1197
    i = 11.25

    4) Now that we have the value of i, substitute it into one of the original equations to find the value of c. We'll use the first equation:

    60c - 91(11.25) = 7
    60c - 1031.25 = 7
    60c = 1031.25 + 7
    60c = 1038.25
    c = 1038.25/60
    c = 17.305

    ### Answer: c = 17.305, i = 11.25

Expected answer: {c: 1931/1048, i: 2087/1834}

Correct? No

🔗 Problem

Problem: Find the values of e and v that satisfy the following two simultaneous linear equations: 1) 71*v - 37*e = 69 2) 41*e + 76*v = 184

Llama 3 8B:

    Let's solve the system of linear equations.

    We can solve the first equation for v:

    v = (69 + 37*e) / 71

    Now, substitute this expression for v into the second equation:

    41*e + 76*((69 + 37*e) / 71) = 184

    Multiply both sides by 71 to eliminate the fraction:

    2871*e + 10676 = 12964

    Subtract 12964 from both sides:

    2871*e = 2288

    Divide both sides by 2871:

    e = 2288 / 2871

    e ≈ 0.80

    Now that we have found e, we can find v by substituting e back into one of the original equations. We'll use the first equation:

    71*v - 37*0.80 = 69

    71*v - 29.6 = 69

    Add 29.6 to both sides:

    71*v = 98.6

    Divide both sides by 71:

    v = 98.6 / 71

    v ≈ 1.39

    ### Answer: e ≈ 0.80, v ≈ 1.39

Expected answer: {e: 7820/5723, v: 9637/5723}

Correct? No

🔗 Problem

Problem: What are the values of 'd' and 'v' in the following system of equations? The sum of 25 times 'v' and 69 times 'd' equals 113. The sum of 26 times 'd' and 42 times 'v' equals 85.

Llama 3 8B:

    Let's solve the system of equations step by step.

    From the first equation, we can write:

    25v + 69d = 113

    From the second equation, we can write:

    26d + 42v = 85

    Now, we can multiply the first equation by 2 and the second equation by 1 to make the coefficients of 'd' the same:

    50v + 138d = 226
    26d + 42v = 85

    Subtract the second equation from the first equation to eliminate 'v':

    138d - 26d = 226 - 85
    112d = 141

    Now, divide both sides by 112:

    d = 141/112
    d = 1.265625

    Now that we have the value of 'd', we can substitute it into one of the original equations to find the value of 'v'. We'll use the first equation:

    25v + 69(1.265625) = 113

    Simplify the right-hand side:

    25v + 88.4375 = 113

    Subtract 88.4375 from both sides:

    25v = 24.5625

    Divide both sides by 25:

    v = 24.5625/25
    v = 0.9825

    ### Answer: d = 1.265625, v = 0.9825

Expected answer: {d: 2621/2248, v: 2927/2248}

Correct? No

🔗 Problem

Problem: Solve the following equations for g and z: 43 * z - 91 * g = 33 72 * g - 3 * z = 68

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply both sides of the first equation by 91 to get:

    3917z - 8281g = 2973

    Now, we can multiply both sides of the second equation by 3 to get:

    216g - 9z = 204

    Now, we can add the two equations to eliminate the z variable:

    3917z - 8281g + 216g - 9z = 2973 + 204

    Combine like terms:

    3908z - 8065g = 3177

    Now, we can divide both sides by 3908 to get:

    z = (3177 + 8065g) / 3908

    Now, substitute this expression for z into one of the original equations. Let's use the first equation:

    43z - 91g = 33

    Substitute the expression for z:

    43((3177 + 8065g) / 3908) - 91g = 33

    Multiply both sides by 3908 to eliminate the fraction:

    16141 + 34835g - 8281g = 12916

    Combine like terms:

    -4806g = -3215

    Divide both sides by -4806:

    g = 3215 / 4806

    g = 0.668

    Now that we have found g, we can substitute this value back into one of the original equations to find z. Let's use the first equation again:

    43z - 91g = 33

    Substitute the value of g:

    43z - 91(0.668) = 33

    Multiply both sides by 100 to eliminate the decimal:

    4300z - 9132 = 3300

    Add 9132 to both sides:

    4300z = 9432

    Divide both sides by 4300:

    z = 9432 / 4300

    z = 2.2

    ### Answer: g = 0.668, z = 2.2

Expected answer: {g: 3023/2823, z: 8564/2823}

Correct? No

🔗 Problem

Problem: Alex's and Brad's baskets contained c cherries and f figs respectively. From an old recipe book, it stated that cherries multiplied by 50 multiplied by the quantity of figs that multiplied by 12, which altogether would weigh about 92 grams. Another recipe book stated that cherries multiplied by 36 minus figs multiplied by 21 should weigh about 34 grams. Can you find the quantity of cherries (c) and figs (f)? Use the following system of equations to solve: 50c + 12f = 92 36c - 21f = 34.

Llama 3 8B:

    Let's solve the system of equations.

    First, we can multiply both sides of the second equation by 12 to make the coefficients of f equal:

    432c - 252f = 408

    Now, we can subtract the first equation from the modified second equation to eliminate f:

    432c - 50c - 252f + 12f = 408 - 92
    382c = 316

    Now, we can divide both sides by 382 to solve for c:

    c = 316/382
    c = 8

    Now that we have found c, we can substitute it into one of the original equations to find f. We'll use the first equation:

    50c + 12f = 92
    50(8) + 12f = 92
    400 + 12f = 92

    Subtract 400 from both sides:

    12f = -308

    Divide both sides by -12:

    f = 308/12
    f = 25.67

    Since f cannot be a fraction, we can round it to the nearest whole number. In this case, f = 26.

    ### Answer: c = 8, f = 26.

Expected answer: {c: 30/19, f: 62/57}

Correct? No

🔗 Problem

Problem: Here are the equations you'll need to solve (remember, the goal is to find the values of u and d): 1) 87u - 75d = 7 2) 85d - 82u = 54

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for u:

    u = (7 + 75d) / 87

    Now, substitute this expression for u into the second equation:

    85d - 82((7 + 75d) / 87) = 54

    Multiply both sides of the equation by 87 to eliminate the fraction:

    7535d - 82(7 + 75d) = 4716

    Expand and simplify:

    7535d - 574 - 6150d = 4716

    Combine like terms:

    -8615d = -1028

    Divide both sides by -8615:

    d = 1028 / 8615

    d = 0.12

    Now that we have found d, we can substitute this value back into one of the original equations to find u. We'll use the first equation:

    87u - 75(0.12) = 7

    87u - 9 = 7

    Add 9 to both sides:

    87u = 16

    Divide both sides by 87:

    u = 16 / 87

    u = 0.184

    ### Answer: u = 0.184, d = 0.12.

Expected answer: {d: 5272/1245, u: 929/249}

Correct? No

🔗 Problem

Problem: Bill is trying to decipher a secret code. He manages to translate two sentences into the following mathematical expressions: (75 * his unknown number a) - (4 * his unknown number i) equals 42, and (10 * i) + (13 * a) equals 160. Using these equations, can you figure out the values of i and a for him?

Llama 3 8B:

    Let's start by solving the first equation:

    (75 * a) - (4 * i) = 42

    We can add (4 * i) to both sides to get:

    (75 * a) = 42 + (4 * i)

    Now, we can subtract 42 from both sides to get:

    75a = 42 + 4i

    Next, we can subtract 4i from both sides to get:

    75a - 4i = 42

    Now, we can divide both sides by 75 to get:

    a - (4/75)i = 42/75

    Now, let's move on to the second equation:

    (10 * i) + (13 * a) = 160

    We can subtract (13 * a) from both sides to get:

    (10 * i) = 160 - (13 * a)

    Now, we can divide both sides by 10 to get:

    i = (160 - 13a) / 10

    Now, we can substitute this expression for i into the first equation:

    (75 * a) - (4 * ((160 - 13a) / 10)) = 42

    We can multiply both sides by 10 to get rid of the fraction:

    (750 * a) - (4 * (160 - 13a)) = 420

    Now, we can expand the right-hand side:

    (750 * a) - 640 + 52a = 420

    Now, we can add 640 to both sides to get:

    (750 * a) + 52a = 1060

    Now, we can combine like terms:

    802a = 1060

    Now, we can divide both sides by 802 to get:

    a = 1060/802

    a = 1.32

    Now that we have found a, we can substitute it into one of the original equations to find i. Let's use the second equation:

    (10 * i) + (13 * 1.32) = 160

    We can simplify the right-hand side:

    (10 * i) + 17.16 = 160

    Now, we can subtract 17.16 from both sides to get:

    (10 * i) = 142.84

    Now, we can divide both sides by 10 to get:

    i = 14.284

    So, the values of i and a are:

    i = 14.284
    a = 1.32

    ### Answer: i = 14.284, a = 1.32

Expected answer: {a: 530/401, i: 5727/401}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of p and c: 37 * p + 74 * c = 183 27 * c - 18 * p = 13

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of p's in both equations are the same:

    1) Multiply the first equation by 18:
    666p + 1332c = 3276
    2) Multiply the second equation by 74:
    198c - 324p = 962

    Now, we can subtract the second equation from the first equation to eliminate the p variable:

    666p + 1332c - (198c - 324p) = 3276 - 962
    666p + 1332c - 198c + 324p = 2314
    690p + 1134c = 2314

    Now, we can solve for p:

    690p = 2314 - 1134c
    p = (2314 - 1134c) / 690

    Now, substitute the expression for p into one of the original equations, say the first equation:

    37 * ((2314 - 1134c) / 690) + 74c = 183

    Simplify the equation:

    37 * (2314 - 1134c) / 690 + 74c = 183
    1373 - 4263c / 19 + 74c = 183

    Multiply both sides by 19 to eliminate the fraction:

    26067 - 4263c + 1414c = 3483
    12494 - 285c = 3483

    Now, subtract 3483 from both sides:

    12494 - 285c - 3483 = 0
    90011 - 285c = 0

    Now, divide both sides by -285:

    c = 90011 / 285
    c = 316

    Now that we have the value of c, we can find the value of p:

    p = (2314 - 1134c) / 690
    p = (2314 - 1134 * 316) / 690
    p = (2314 - 357624) / 690
    p = -356310 / 690
    p = -516

    ### Answer: p = -516, c = 316

Expected answer: {c: 3775/2331, p: 3979/2331}

Correct? No

🔗 Problem

Problem: Determine the values of k and p from the following system of equations: (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for k:

    48k - 30p = 37
    48k = 30p + 37
    k = (30p + 37) / 48

    Now, substitute this expression for k into the second equation:

    16p + 33((30p + 37) / 48) = 105

    Multiply both sides by 48 to eliminate the fraction:

    768p + 33(30p + 37) = 5040

    Expand and simplify:

    768p + 990p + 1217 = 5040
    2058p + 1217 = 5040

    Subtract 1217 from both sides:

    2058p = 3823

    Divide both sides by 2058:

    p = 3823 / 2058
    p = 1.86 (approximately)

    Now that we have found p, we can substitute it back into one of the original equations to find k. We'll use the first equation:

    48k - 30p = 37
    48k - 30(1.86) = 37

    Multiply 30(1.86) = 56.8:

    48k - 56.8 = 37

    Add 56.8 to both sides:

    48k = 93.8

    Divide both sides by 48:

    k = 93.8 / 48
    k = 1.96 (approximately)

    So, the values of k and p are approximately:

    k ≈ 1.96
    p ≈ 1.86

    ### Answer: k ≈ 1.96, p ≈ 1.86.

Expected answer: {k: 1871/879, p: 1273/586}

Correct? No

🔗 Problem

Problem: Consider the following pair of equations. 1. 75v - 69f = 14 2. 46f + 53v = 110 Determine the values for v and f that satisfy these simultaneous equations.

Llama 3 8B:

    Let's solve the system of equations using the method of substitution or elimination.

    First, let's multiply equation (1) by 46 to make the coefficients of f in both equations the same:

    46(75v - 69f = 14)
    3465v - 3186f = 686

    Now, add equation (2) to the modified equation (1):

    3465v - 3186f = 686
    46f + 53v = 110
    -------------------
    3511v - 3186f = 796

    Now, divide both sides by -3186:

    v = (796 + 3186f) / 3511

    Substitute this expression for v into one of the original equations, say equation (1):

    75((796 + 3186f) / 3511) - 69f = 14

    Multiply both sides by 3511 to eliminate the fraction:

    267750 + 239610f - 47565f = 15186

    Combine like terms:

    219285 + 960f = 15186

    Subtract 219285 from both sides:

    960f = -70799

    Divide both sides by -960:

    f = 73.75

    Now that we have found f, we can find v by substituting f into the expression we found earlier:

    v = (796 + 3186(73.75)) / 3511
    v = (796 + 23625) / 3511
    v = 24021 / 3511
    v = 6.85

    ### Answer: v = 6.85, f = 73.75

Expected answer: {f: 7508/7107, v: 358/309}

Correct? No

🔗 Problem

Problem: Determine the values of o and g from the following system of equations: 7 * o + 13 * g = 131 89 * g - 70 * o = 37.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for g:

    g = (37 + 70o) / 89

    Now, substitute this expression for g into the first equation:

    7o + 13((37 + 70o) / 89) = 131

    Multiply both sides by 89 to eliminate the fraction:

    637o + 13(37 + 70o) = 11693

    Expand and simplify:

    637o + 481 + 910o = 11693

    Combine like terms:

    1547o = 11112

    Divide both sides by 1547:

    o = 11112 / 1547

    o = 7.2

    Now that we have found o, we can find g by substituting o into one of the original equations. We'll use the second equation:

    89g - 70(7.2) = 37

    89g - 504 = 37

    Add 504 to both sides:

    89g = 541

    Divide both sides by 89:

    g = 541 / 89

    g = 6.1

    ### Answer: o = 7.2, g = 6.1

Expected answer: {g: 449/73, o: 3726/511}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of d and k: 88 * d - 60 * k = 38 33 * k - 11 * d = 46.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply both equations by necessary multiples such that the coefficients of d's in both equations are the same:

    1) Multiply the first equation by 11:
    968d - 660k = 418
    2) Multiply the second equation by 60:
    1980k - 660d = 2760

    Now, we can subtract the first equation from the second equation to eliminate d:

    (1980k - 660d) - (968d - 660k) = 2760 - 418
    1980k - 660d - 968d + 660k = 2342
    2012k - 1320d = 2342

    Now, we can solve for k:

    k = (2342 + 1320d) / 2012

    Now, substitute this expression for k into one of the original equations. We'll use the first equation:

    88d - 60((2342 + 1320d) / 2012) = 38

    Multiply both sides by 2012 to eliminate the fraction:

    176,960d - 140,320 = 76,544

    Now, subtract 76,544 from both sides:

    176,960d = 64,416

    Now, divide both sides by 176,960:

    d = 64,416 / 176,960
    d = 0.364

    Now that we have the value of d, we can find the value of k:

    k = (2342 + 1320d) / 2012
    k = (2342 + 1320(0.364)) / 2012
    k = (2342 + 480.48) / 2012
    k = 2822.48 / 2012
    k = 1.405

    ### Answer: d = 0.364, k = 1.405

Expected answer: {d: 669/374, k: 203/102}

Correct? No

🔗 Problem

Problem: Consider the following system of equations, calculate the values of y and z: 24 * z + 72 * y = 139, 2 * z + 82 * y = 96.

Llama 3 8B:

    Let's solve the system of equations using the method of elimination.

    First, we can multiply the two equations by necessary multiples such that the coefficients of y's in both equations are the same:

    1) Multiply the first equation by 41 (which is the coefficient of y in the second equation):
    24z + 72y = 139
    41(24z + 72y) = 41(139)
    576z + 2952y = 5671

    2) Multiply the second equation by 1 (no need to multiply):
    2z + 82y = 96

    Now, subtract the second equation from the first equation:

    (576z + 2952y) - (2z + 82y) = 5671 - 96
    574z + 2870y = 5575

    Now, simplify the equation:

    574z = 5575 - 2870y
    z = (5575 - 2870y) / 574

    Now, substitute the value of z in one of the original equations. We'll use the first equation:

    24z + 72y = 139
    24((5575 - 2870y) / 574) + 72y = 139

    Simplify the equation:

    13920 - 103800y + 72y = 139
    13920 - 103728y = 139
    103728y = 13920 + 139
    103728y = 13959
    y = 13959 / 103728
    y ≈ 0.134

    Now that we have the value of y, we can find the value of z:

    z = (5575 - 2870y) / 574
    z = (5575 - 2870(0.134)) / 574
    z = (5575 - 383.32) / 574
    z = 5191.68 / 574
    z ≈ 9.03

    ### Answer: y ≈ 0.134, z ≈ 9.03

Expected answer: {y: 1013/912, z: 2243/912}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the variables v and o: (87 * o) - (29 * v) = 1 and (8 * v) + (30 * o) = 91.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can rewrite the equations in a more convenient form:

    1) 87o - 29v = 1
    2) 8v + 30o = 91

    Now, we can solve the first equation for o:

    o = (1 + 29v) / 87

    Substitute this expression for o into the second equation:

    8v + 30((1 + 29v) / 87) = 91

    Multiply both sides by 87 to eliminate the fraction:

    8v * 87 + 30(1 + 29v) = 91 * 87

    Expand and simplify:

    696v + 30 + 870v = 7937

    Combine like terms:

    1566v + 30 = 7937

    Subtract 30 from both sides:

    1566v = 7907

    Divide both sides by 1566:

    v = 7907 / 1566

    v = 5

    Now that we have found v, we can find o by substituting v into one of the original equations. We'll use the first equation:

    o = (1 + 29(5)) / 87

    o = (1 + 145) / 87

    o = 146 / 87

    o = 2

    So, the values of v and o are:

    v = 5
    o = 2

    ### Answer: v = 5, o = 2

Expected answer: {o: 2647/1566, v: 2629/522}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for h and p: The first equation is (23 * h) - (46 * p) = 58 The second equation is (11 * p) + (23 * h) = 124.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can simplify the first equation by multiplying both sides by 1 to get rid of the parentheses:

    23h - 46p = 58

    Next, we can simplify the second equation by multiplying both sides by 1 to get rid of the parentheses:

    11p + 23h = 124

    Now, we can solve for h in the first equation:

    23h = 58 + 46p

    Divide both sides by 23:

    h = (58 + 46p) / 23

    Now, substitute this expression for h into the second equation:

    11p + 23((58 + 46p) / 23) = 124

    Simplify the equation:

    11p + 58 + 46p = 124

    Combine like terms:

    57p + 58 = 124

    Subtract 58 from both sides:

    57p = 66

    Divide both sides by 57:

    p = 66 / 57

    p = 1.16 (approximately)

    Now that we have found p, we can substitute it back into one of the original equations to find h. We'll use the first equation:

    23h - 46(1.16) = 58

    Simplify:

    23h - 53.36 = 58

    Add 53.36 to both sides:

    23h = 111.36

    Divide both sides by 23:

    h = 111.36 / 23

    h = 4.84 (approximately)

    ### Answer: h ≈ 4.84, p ≈ 1.16.

Expected answer: {h: 2114/437, p: 22/19}

Correct? No

🔗 Problem

Problem: If the following system of equations represents the relationship between integers d and f, determine their values: 1) 19d + 6f = 120, 2) 90d - 42f = 69.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply equation (2) by 2 to make the coefficients of f in both equations the same:

    2) 180d - 84f = 138

    Now, we can add equation (1) and equation (2) to eliminate the f term:

    (19d + 6f = 120) + (180d - 84f = 138)

    This gives us:

    199d = 258

    Now, we can solve for d:

    d = 258/199 = 1.3 (not an integer, so we'll try to eliminate the fraction)

    d = 129/99 = 1 1/3 (not an integer, so we'll try to eliminate the fraction)

    d = 128/98 = 1 1/7 (not an integer, so we'll try to eliminate the fraction)

    d = 127/97 = 1 1/9 (not an integer, so we'll try to eliminate the fraction)

    d = 126/96 = 1 1/2 (integer!)

    So, d = 1 1/2 = 3/2 = 1.5 (not an integer, so we'll try to eliminate the fraction)

    d = 1

    Now that we have the value of d, we can substitute it into one of the original equations to solve for f. We'll use equation (1):

    19d + 6f = 120

    19(1) + 6f = 120

    6f = 120 - 19 = 101

    f = 101/6 = 16 5/6 (not an integer, so we'll try to eliminate the fraction)

    f = 16

    So, the values of d and f are:

    d = 1
    f = 16

    ### Answer: d = 1, f = 16.

Expected answer: {d: 909/223, f: 3163/446}

Correct? No

🔗 Problem

Problem: Here's a problem: A system of linear equations is given by the following formulas: 1) 42 * m + 55 * r = 127 2) 66 * m - 52 * r = 44 Can you solve this system to find the values of 'r' and 'm'?

Llama 3 8B:

    Let's solve the system of linear equations step by step.

    First, we can multiply equation (1) by 2 and equation (2) by 1 to make the coefficients of 'r' in both equations the same:

    1) 84 * m + 110 * r = 254
    2) 66 * m - 52 * r = 44

    Now, we can subtract equation (2) from equation (1) to eliminate 'm':

    (84 * m + 110 * r) - (66 * m - 52 * r) = 254 - 44
    84 * m + 110 * r - 66 * m + 52 * r = 210
    18 * m + 162 * r = 210

    Next, we can subtract 162 * r from both sides to get:

    18 * m = 210 - 162 * r
    18 * m = 48 - 162 * r

    Now, we can divide both sides by 18 to solve for 'm':

    m = (48 - 162 * r) / 18

    Now that we have the expression for 'm', we can substitute it into one of the original equations to solve for 'r'. Let's use equation (1):

    42 * m + 55 * r = 127
    42 * ((48 - 162 * r) / 18) + 55 * r = 127

    Simplifying the equation, we get:

    24 + 55 * r = 127
    55 * r = 103
    r = 103 / 55
    r = 1.87

    Now that we have the value of 'r', we can substitute it back into the expression for 'm' to find the value of 'm':

    m = (48 - 162 * 1.87) / 18
    m = (48 - 303.54) / 18
    m = -255.54 / 18
    m = -14.23

    ### Answer: m = -14.23, r = 1.87

Expected answer: {m: 1504/969, r: 363/323}

Correct? No

🔗 Problem

Problem: Determine the values of n and w that satisfy the following system of linear equations simultaneously: 31n + 64w = 120 57w + 71n = 173

Llama 3 8B:

    To solve this system of linear equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

    First, we will multiply the two equations by necessary multiples such that the coefficients of n's in both equations are the same:

    1) Multiply the first equation by 71 and the second equation by 31:

    2177n + 4480w = 8480
    1771w + 5041n = 5373

    2) Subtract the second equation from the first equation to eliminate n:

    4480w - 1771w = 8480 - 5373
    2711w = 3107

    3) Divide both sides by 2711:

    w = 3107/2711
    w = 1.15

    4) Now that we have the value of w, substitute it into one of the original equations to find the value of n. We will use the first equation:

    31n + 64(1.15) = 120

    5) Simplify the equation:

    31n + 76.4 = 120

    6) Subtract 76.4 from both sides:

    31n = 43.6

    7) Divide both sides by 31:

    n = 43.6/31
    n = 1.41

    ### Answer: n = 1.41, w = 1.15.

Expected answer: {n: 4232/2777, w: 3157/2777}

Correct? No

🔗 Problem

Problem: Determine the values of u and a from the following system of linear equations: 1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31.

Llama 3 8B:

    Let's solve the system of linear equations step by step.

    We have two equations:

    1) 72a + 26u = 112
    2) 76u - 77a = 31

    We can solve this system using substitution or elimination. Let's use elimination.

    First, we can multiply equation (1) by 77 and equation (2) by 72 to make the coefficients of a in both equations the same:

    1) 5548a + 1972u = 8656
    2) 5472u - 5516a = 2184

    Now, we can subtract equation (2) from equation (1) to eliminate a:

    (5548a + 1972u) - (5472u - 5516a) = 8656 - 2184
    5548a + 1972u - 5472u + 5516a = 8656 - 2184
    11064a = 6472

    Now, we can solve for a:

    a = 6472 / 11064
    a = 0.58

    Now that we have the value of a, we can substitute it into one of the original equations to solve for u. Let's use equation (1):

    72a + 26u = 112
    72(0.58) + 26u = 112
    41.76 + 26u = 112

    Subtract 41.76 from both sides:

    26u = 70.24

    Divide both sides by 26:

    u = 70.24 / 26
    u = 2.7

    ### Answer: u = 2.7, a = 0.58

Expected answer: {a: 3853/3737, u: 5428/3737}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of b and n: the first equation is 54n + 18b = 143 and the second equation is 87n - 93b = 48.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of b's in both equations are the same:

    1) Multiply the first equation by 93:
    93(54n + 18b = 143) => 5493n + 1674b = 13331

    2) Multiply the second equation by 18:
    18(87n - 93b = 48) => 1566n - 1674b = 864

    Now, we can subtract the second equation from the first equation to eliminate the term with b:

    (5493n + 1674b = 13331) - (1566n - 1674b = 864)
    => 6937n = 12467

    Now, we can solve for n:
    6937n = 12467
    n = 12467/6937
    n = 1.8

    Now that we have the value of n, we can substitute it into one of the original equations to find the value of b. We'll use the first equation:

    54n + 18b = 143
    54(1.8) + 18b = 143
    97.2 + 18b = 143

    Subtract 97.2 from both sides:
    18b = 45.8

    Divide both sides by 18:
    b = 45.8/18
    b = 2.55

    ### Answer: b = 2.55, n = 1.8

Expected answer: {b: 3283/2196, n: 4721/2196}

Correct? No

🔗 Problem

Problem: Given the following system of equations about a company's production economics, where e represents the cost of electricity and p is the cost of petroleum: 53 * e + 7 * p = 103 69 * e - 88 * p = 6 What are the costs of electricity (e) and petroleum (p)?

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of p's in both equations are the same:

    1) Multiply the first equation by 88:
    53 * e + 7 * p = 103
    53 * e + 7 * p = 103
    88 * 53 * e + 88 * 7 * p = 88 * 103

    2) Multiply the second equation by 7:
    69 * e - 88 * p = 6
    7 * 69 * e - 7 * 88 * p = 7 * 6

    Now, we can subtract the second equation from the first equation:

    (88 * 53 * e + 88 * 7 * p) - (7 * 69 * e - 7 * 88 * p) = (88 * 103) - (7 * 6)
    88 * 53 * e + 88 * 7 * p - 7 * 69 * e + 7 * 88 * p = 88 * 103 - 7 * 6
    (88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6 + 88 * 7 * p - 7 * 88 * p
    (88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6 + 88 * (7 * p - 7 * p)
    (88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6 + 88 * 0
    (88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103 - 42
    (88 * 53 - 7 * 69) * e = 88 * 103

Expected answer: {e: 9106/5147, p: 6789/5147}

Correct? No

🔗 Problem

Problem: Consider the following pair of linear equations. First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Find the values of p and s that satisfy both equations.

Llama 3 8B:

    Let's solve the system of linear equations.

    First, we can multiply the first equation by 24 to make the coefficients of p in both equations the same:

    24((18 * p) - (7 * s)) = 24 * 21
    432p - 168s = 504

    Now, we can subtract the second equation from the modified first equation:

    432p - 168s = 504
    -(51s - 24p) = 14

    Combine like terms:

    432p - 168s - 51s + 24p = 504 - 14
    432p - 219s = 490

    Now, we can solve for p:

    432p = 490 + 219s
    p = (490 + 219s) / 432

    Now, substitute this expression for p into the original first equation:

    ((18 * ((490 + 219s) / 432)) - (7 * s)) = 21

    Simplify and solve for s:

    (18 * (490 + 219s) / 432) - 7s = 21
    (1710 + 3918s) / 432 - 7s = 21
    3918s - 7s = 21 * 432 - 1710
    3911s = 9261 - 1710
    3911s = 7551
    s = 7551 / 3911
    s = 1.94 (approximately)

    Now that we have the value of s, we can find the value of p:

    p = (490 + 219 * 1.94) / 432
    p = (490 + 423.66) / 432
    p = 913.66 / 432
    p = 2.11 (approximately)

    ### Answer: p ≈ 2.11, s ≈ 1.94.

Expected answer: {p: 1169/750, s: 126/125}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for c and w: The first equation is 59 times c minus 34 times w is equal to 84. The second equation is 11 times c plus 42 times w is equal to 98.

Llama 3 8B:

    Let's solve the system of equations step by step.

    We have two equations:

    1) 59c - 34w = 84
    2) 11c + 42w = 98

    We can solve this system of equations using the method of substitution or elimination. Here, we'll use the elimination method.

    First, we'll multiply both equations by necessary multiples such that the coefficients of w's in both equations are the same:

    1) 59c - 34w = 84
     Multiply equation (1) by 3 and equation (2) by 2:
    3(59c - 34w = 84) => 177c - 102w = 252
    2) 11c + 42w = 98
     Multiply equation (2) by 3:
    3(11c + 42w = 98) => 33c + 126w = 294

    Now, subtract equation (2) from equation (1):

    (177c - 102w = 252) - (33c + 126w = 294)
    => 144c - 228w = -42

    Now, we have a new equation:

    144c - 228w = -42

    Now, we'll multiply equation (1) by 1 and equation (2) by 2:
    1(59c - 34w = 84) => 59c - 34w = 84
    2(11c + 42w = 98) => 22c + 84w = 196

    Now, add equation (1) and equation (2):

    (59c - 34w = 84) + (22c + 84w = 196)
    => 81c + 50w = 280

    Now, we have a new equation:

    81c + 50w = 280

    Now, we'll solve the system of equations by solving the above two equations:

    144c - 228w = -42
    81c + 50w = 280

    Now, multiply equation (2) by 3:
    3(81c + 50w = 280) => 243c + 150w = 840

    Now, subtract equation (1) from equation (2):

    (243c + 150w = 840) - (144c - 228w = -42)
    => 387c + 378w = 882

    Now, divide both sides by 387:
    c = 882/387
    c = 2.28

    Now, substitute the value of c in one of the original equations, say equation (1):

    59c - 34w = 84
    59(2.28) - 34w = 84
    133.32 - 34w = 84

    Now, subtract 133.32 from both sides:
    -34w = -49.32

    Now, divide both sides by -34:
    w = 49.32/34
    w = 1.45

    ### Answer: c = 2.28, w = 1.45

Expected answer: {c: 1715/713, w: 2429/1426}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of f and z: First equation is 45 * f + 42 * z = 101, Second equation is 60 * z - 42 * f = 13.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of f's in both equations are the same:

    1) Multiply the first equation by 42 and the second equation by 45:

    1) 1890f + 1764z = 4282
    2) 2700z - 1890f = 585

    Now, we can subtract the second equation from the first equation to eliminate the f variable:

    1890f + 1764z = 4282
    - (2700z - 1890f = 585)

    This gives us:

    3800z = 3697

    Now, we can solve for z:

    z = 3697/3800
    z = 0.9755

    Now that we have the value of z, we can substitute it into one of the original equations to solve for f. We'll use the first equation:

    45f + 42z = 101
    45f + 42(0.9755) = 101

    Simplifying the equation:

    45f + 41.71 = 101

    Subtracting 41.71 from both sides:

    45f = 59.29

    Dividing both sides by 45:

    f = 59.29/45
    f = 1.315

    ### Answer: f = 1.315, z = 0.9755

Expected answer: {f: 919/744, z: 1609/1488}

Correct? No

🔗 Problem

Problem: Calculate the values of p and u from the following system of equations: 26 * p - 21 * u = 6 15 * p + 58 * u = 83.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for p:

    26p - 21u = 6
    26p = 6 + 21u
    p = (6 + 21u) / 26

    Now, substitute this expression for p into the second equation:

    15((6 + 21u) / 26) + 58u = 83

    Multiply both sides by 26 to eliminate the fraction:

    15(6 + 21u) + 58u * 26 = 83 * 26

    Expand and simplify:

    90 + 315u + 1492u = 2158

    Combine like terms:

    2507u = 2068

    Divide by 2507:

    u = 2068 / 2507
    u = 0.826

    Now that we have found u, we can substitute it back into one of the original equations to find p. We'll use the first equation:

    26p - 21u = 6
    26p - 21(0.826) = 6

    Simplify:

    26p - 17.346 = 6

    Add 17.346 to both sides:

    26p = 23.346

    Divide by 26:

    p = 23.346 / 26
    p = 0.900

    ### Answer: p = 0.900, u = 0.826.

Expected answer: {p: 2091/1823, u: 2068/1823}

Correct? No

🔗 Problem

Problem: Solve for the values of n and s using these two simultaneous equations: 1) 92 * n - 38 * s = 62 2) 59 * n + 8 * s = 75

Llama 3 8B:

    Let's solve the system of equations.

    We can start by multiplying equation (1) by 8 and equation (2) by 38 to make the coefficients of s in both equations the same:

    1) 736n - 304s = 496
    2) 2236n + 304s = 2860

    Now, we can subtract equation (1) from equation (2) to eliminate the s term:

    2236n - 736n = 2860 - 496
    1500n = 2364

    Now, we can solve for n:

    n = 2364/1500
    n = 1.576

    Now that we have the value of n, we can substitute it into one of the original equations to solve for s. We'll use equation (1):

    92n - 38s = 62
    92(1.576) - 38s = 62
    148.352 - 38s = 62

    Now, we can solve for s:

    -38s = -86.352
    s = 86.352/38
    s = 2.272

    ### Answer: n = 1.576, s = 2.272

Expected answer: {n: 1673/1489, s: 1621/1489}

Correct? No

🔗 Problem

Problem: Solving the following pairs of simultaneous equations, what would be the values for e and z? The equations are: 87 * z - 35 * e = 63 and 81 * z + 58 * e = 154.

Llama 3 8B:

    Let's solve the system of equations step by step.

    We have:

    1) 87z - 35e = 63
    2) 81z + 58e = 154

    First, we can multiply equation (1) by 58 and equation (2) by 35 to make the coefficients of e in both equations the same:

    1) 5049z - 1990e = 3633
    2) 2835z + 2030e = 5390

    Now, we can subtract equation (1) from equation (2) to eliminate the e term:

    2835z + 2030e - 5049z + 1990e = 5390 - 3633
    -2814z = 3407

    Now, divide both sides by -2814:

    z = -3407/2814

    Now that we have the value of z, we can substitute it into one of the original equations to find the value of e. We'll use equation (1):

    87z - 35e = 63
    87(-3407/2814) - 35e = 63

    Simplify:

    -29919/2814 - 35e = 63

    Multiply both sides by -2814 to eliminate the fraction:

    29919 + 2814(35e) = -2814(63)

    Simplify:

    29919 + 123150e = -18486

    Subtract 29919 from both sides:

    123150e = -48405

    Divide both sides by 123150:

    e = -48405/123150

    ### Answer: z = -3407/2814, e = -48405/123150

Expected answer: {e: 2765/2627, z: 9044/7881}

Correct? No

🔗 Problem

Problem: To find the values of h and t, solve the following system of simultaneous linear equations: (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18.

Llama 3 8B:

    Let's solve the system of simultaneous linear equations.

    We have two equations:

    1) 11t + 44h = 110
    2) 98t - 36h = 18

    We can solve this system using substitution or elimination. Let's use elimination.

    First, we can multiply equation (1) by 3 and equation (2) by 1 to make the coefficients of h in both equations the same:

    1) 33t + 132h = 330
    2) 98t - 36h = 18

    Now, we can subtract equation (2) from equation (1) to eliminate h:

    (33t + 132h) - (98t - 36h) = 330 - 18
    33t + 132h - 98t + 36h = 312
    -65t + 168h = 312

    Now, we can solve for t:

    -65t = 312 - 168h
    t = (312 - 168h) / -65

    Now that we have the value of t, we can substitute it into one of the original equations to solve for h. Let's use equation (1):

    11t + 44h = 110
    11((312 - 168h) / -65) + 44h = 110

    Simplifying the equation:

    -66 + 44h + 44h = 110
    88h = 176
    h = 176 / 88
    h = 2

    Now that we have the values of h and t, we can substitute them back into the original equations to verify:

    1) 11t + 44h = 110
    11(312/65) + 44(2) = 110
    44 + 88 = 132 ≠ 110 (Error)

    2) 98t - 36h = 18
    98(312/65) - 36(2) = 18
    176 - 72 = 104 ≠ 18 (Error)

    It seems that there is an error in the system of equations. The values of h and t do not satisfy both equations.

    ### Answer: No solution exists.

Expected answer: {h: 481/214, t: 108/107}

Correct? No

🔗 Problem

Problem: Solve the following system of linear equations to find the values of b and o: ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85.

Llama 3 8B:

    Let's solve the system of linear equations step by step.

    First, we can rewrite the equations in standard form:

    Equation 1: 69b - 50o = 55
    Equation 2: 41o + 18b = 85

    Next, we can multiply Equation 1 by 41 and Equation 2 by 50 to make the coefficients of o in both equations the same:

    Equation 1 (multiplied by 41): 2789b - 2050o = 2265
    Equation 2 (multiplied by 50): 2050o + 900b = 4250

    Now, we can subtract Equation 1 from Equation 2 to eliminate the o variable:

    (2050o + 900b) - (2789b - 2050o) = 4250 - 2265
    900b - 2789b = 4250 - 2265
    -1891b = 1985

    Now, we can solve for b:

    -1891b = -1985
    b = 1985 / 1891
    b ≈ 1.05

    Now that we have the value of b, we can substitute it into one of the original equations to solve for o. We'll use Equation 1:

    69b - 50o = 55
    69(1.05) - 50o = 55
    73.5 - 50o = 55

    Now, we can solve for o:

    -50o = -18.5
    o = 18.5 / 50
    o ≈ 0.37

    So, the values of b and o are approximately 1.05 and 0.37, respectively.

    ### Answer: b ≈ 1.05, o ≈ 0.37

Expected answer: {b: 6505/3729, o: 1625/1243}

Correct? No

🔗 Problem

Problem: Solve the following system of equations to find the values of p and q: 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of p's in both equations are the same:

    1) Multiply the first equation by 5 and the second equation by 80:
    5 * (67 * q - 80 * p = 65) => 335q - 400p = 325
    80 * (6 * q + 5 * p = 177) => 480q + 400p = 14160

    Now, we can subtract the first equation from the second equation to eliminate the p term:

    (480q + 400p = 14160) - (335q - 400p = 325)
    => 145q = 14035

    Now, we can solve for q:
    q = 14035 / 145
    q = 96.69 (approximately)

    Now that we have the value of q, we can substitute it into one of the original equations to find the value of p. We'll use the first equation:

    67 * q - 80 * p = 65
    67 * 96.69 - 80 * p = 65
    6493.23 - 80 * p = 65

    Now, we can solve for p:
    p = (6493.23 - 65) / 80
    p = 62.69 (approximately)

    So, the values of p and q are approximately 62.69 and 96.69, respectively.

    ### Answer: p ≈ 62.69, q ≈ 96.69.

Expected answer: {p: 11469/815, q: 2897/163}

Correct? No

🔗 Problem

Problem: Find the values of k and f that satisfy the following system of equations: 10 * k + 48 * f = 161 33 * k - 41 * f = 31.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for k:

    10k + 48f = 161
    10k = 161 - 48f
    k = (161 - 48f) / 10

    Now, substitute this expression for k into the second equation:

    33((161 - 48f) / 10) - 41f = 31

    Multiply both sides by 10 to eliminate the fraction:

    330 - 1488f + 41f = 310

    Combine like terms:

    -1447f = -20

    Divide both sides by -1447:

    f = 20/1447

    Now that we have found f, we can substitute this value back into one of the original equations to find k. We'll use the first equation:

    10k + 48(20/1447) = 161

    Multiply both sides by 1447 to eliminate the fraction:

    14470k + 9600 = 233,332

    Subtract 9600 from both sides:

    14470k = 225,732

    Divide both sides by 14470:

    k = 225,732 / 14470

    k = 15.6

    So, the values of k and f that satisfy the system of equations are:

    k = 15.6
    f = 20/1447

    ### Answer: k = 15.6, f = 20/1447.

Expected answer: {f: 5003/1994, k: 8089/1994}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of l and n: The first equation is 31 = 58 * l - n The second equation is 103 = n + 73 * l

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can rewrite the first equation as:

    n = 58l - 31

    Now, substitute this expression for n into the second equation:

    103 = (58l - 31) + 73l

    Combine like terms:

    103 = 131l - 31

    Add 31 to both sides:

    134 = 131l

    Divide both sides by 131:

    l = 134/131

    l = 1.02

    Now that we have the value of l, substitute it back into the expression for n:

    n = 58l - 31
    n = 58(1.02) - 31
    n = 59.24 - 31
    n = 28.24

    So, the values of l and n are:

    l = 1.02
    n = 28.24

    ### Answer: l = 1.02, n = 28.24

Expected answer: {l: 134/131, n: 3711/131}

Correct? No

🔗 Problem

Problem: Find the values of y and j that satisfy the following system of equations: 29y - 28j = 39 25y + 37j = 116

Llama 3 8B:

    To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

    First, we will multiply the two equations by necessary multiples such that the coefficients of j's in both equations are the same:

    1) Multiply the first equation by 37 and the second equation by 28:

    1117y - 1036j = 1431
    700y + 1036j = 3248

    2) Now, subtract the first equation from the second equation to eliminate j:

    700y - 1117y = 3248 - 1431
    -417y = 1817

    3) Now, divide both sides by -417:

    y = -1817/417
    y = -4.33

    4) Now that we have the value of y, substitute it in one of the original equations to find the value of j. We will use the first equation:

    29y - 28j = 39
    29(-4.33) - 28j = 39

    5) Simplify and solve for j:

    -125.97 - 28j = 39
    -28j = 39 + 125.97
    -28j = 165.97
    j = -165.97/28
    j = -5.89

    ### Answer: y = -4.33, j = -5.89

Expected answer: {j: 2389/1773, y: 4691/1773}

Correct? No

🔗 Problem

Problem: Given the following system of equations, solve for u and a: The first equation is 93u - 85a = 74 The second equation is 96u + 17a = 186.

Llama 3 8B:

    Let's solve the system of equations.

    We can start by multiplying the first equation by 17 and the second equation by 85 to make the coefficients of a the same:

    1) 1592u - 1425a = 1262
    2) 8160u + 1445a = 15830

    Now, we can subtract the first equation from the second equation to eliminate the variable a:

    8160u - 1592u = 15830 - 1262
    6568u = 14568

    Now, we can divide both sides by 6568 to solve for u:

    u = 14568/6568
    u = 2.22

    Now that we have the value of u, we can substitute it into one of the original equations to solve for a. Let's use the first equation:

    93u - 85a = 74
    93(2.22) - 85a = 74
    209.46 - 85a = 74

    Now, we can subtract 74 from both sides and then divide both sides by -85 to solve for a:

    -85a = -135.46
    a = 135.46/85
    a = 1.6

    ### Answer: u = 2.22, a = 1.6

Expected answer: {a: 3398/3247, u: 1004/573}

Correct? No

🔗 Problem

Problem: Given the following pair of simultaneous equations, please find out the values of u and g: 97 * u - 61 * g = 15 85 * u + 23 * g = 186

Llama 3 8B:

    To solve this system of linear equations, we can use the method of substitution or elimination. Here, we'll use the elimination method.

    First, we'll multiply both equations by necessary multiples such that the coefficients of g's in both equations are the same:

    1) Multiply the first equation by 23:
    97u - 61g = 15
     Multiply by 23:
    2237u - 1387g = 345

    2) Multiply the second equation by 61:
    85u + 23g = 186
     Multiply by 61:
    5175u + 1387g = 11346

    Now, subtract the first equation from the second equation to eliminate g:

    5175u + 1387g - 2237u + 1387g = 11346 - 345
    2948u = 11001

    Now, divide by 2948:
    u = 11001/2948
    u = 3.73

    Now that we have the value of u, substitute it into one of the original equations to find the value of g. We'll use the first equation:

    97u - 61g = 15
    97(3.73) - 61g = 15
    365.21 - 61g = 15

    Add 61g to both sides:
    365.21 = 15 + 61g

    Subtract 15 from both sides:
    350.21 = 61g

    Divide by 61:
    g = 350.21/61
    g = 5.74

    ### Answer: u = 3.73, g = 5.74

Expected answer: {g: 1863/824, u: 1299/824}

Correct? No

🔗 Problem

Problem: Determine the values of r and b that satisfy the following system of equations. The first equation is (17 * r) + (67 * b) = 103. The second equation is (85 * r) + (67 * b) = 187.

Llama 3 8B:

    Let's solve the system of equations.

    We can rewrite the system as:

    1) 17r + 67b = 103
    2) 85r + 67b = 187

    Subtracting equation (1) from equation (2), we get:

    (85r - 17r) + (67b - 67b) = 187 - 103
    68r = 84

    Dividing both sides by 68, we get:

    r = 84/68
    r = 1.25

    Now that we have the value of r, we can substitute it into one of the original equations to solve for b. Let's use equation (1):

    17r + 67b = 103
    17(1.25) + 67b = 103
    17.25 + 67b = 103

    Subtracting 17.25 from both sides, we get:

    67b = 85.75

    Dividing both sides by 67, we get:

    b = 85.75/67
    b = 1.28

    ### Answer: r = 1.25, b = 1.28

Expected answer: {b: 82/67, r: 21/17}

Correct? No

🔗 Problem

Problem: Given the following system of equations, solve for the values of t and n: 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126.

Llama 3 8B:

    Let's solve the system of equations step by step.

    From equation (1), we can express n in terms of t:

    n = (41 + 54t) / 85

    Now, substitute this expression for n into equation (2):

    (38t) + (30((41 + 54t) / 85)) = 126

    Simplify the equation:

    38t + (1230 + 1620t) / 85 = 126

    Multiply both sides by 85 to eliminate the fraction:

    3230 + 1620t = 10750

    Subtract 3230 from both sides:

    1620t = 7530

    Divide both sides by 1620:

    t = 7530 / 1620

    t = 4.67

    Now that we have the value of t, we can find the value of n:

    n = (41 + 54(4.67)) / 85

    n = (41 + 253.58) / 85

    n = 294.58 / 85

    n = 3.47

    ### Answer: t = 4.67, n = 3.47

Expected answer: {n: 4181/2425, t: 948/485}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of u and q: 1) The result of multiplying 75 by u and subtracting the product of 69 and q is equal to 5. 2) The sum of the product of 48 and u and the product of 25 and q is 140.

Llama 3 8B:

    Let's solve the system of equations step by step.

    Equation 1: 75u - 69q = 5

    Equation 2: 48u + 25q = 140

    We can solve Equation 1 for u:

    u = (5 + 69q) / 75

    Now, substitute this expression for u into Equation 2:

    48((5 + 69q) / 75) + 25q = 140

    Multiply both sides by 75 to eliminate the fraction:

    288 + 1032q + 1875q = 10500

    Combine like terms:

    3007q = 10500 - 288

    q = (10500 - 288) / 3007

    q ≈ 3.48

    Now that we have found q, we can substitute it back into Equation 1 to find u:

    u = (5 + 69(3.48)) / 75

    u ≈ 1.14

    ### Answer: u ≈ 1.14, q ≈ 3.48

Expected answer: {q: 180/91, u: 515/273}

Correct? No

🔗 Problem

Problem: Determine the values of v and x from the following system of equations: ((20 * v) + (17 * x)) = 149 and ((24 * x) - (49 * v)) = 22.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for v:

    20v + 17x = 149

    Subtract 17x from both sides:

    20v = 149 - 17x

    Divide both sides by 20:

    v = (149 - 17x) / 20

    Now, substitute this expression for v into the second equation:

    (24x) - (49((149 - 17x) / 20)) = 22

    Multiply both sides by 20 to eliminate the fraction:

    480x - 14949 + 935x = 440

    Combine like terms:

    1415x = 14989

    Divide both sides by 1415:

    x = 14989 / 1415

    x = 10.6

    Now that we have the value of x, we can substitute it back into the expression for v:

    v = (149 - 17(10.6)) / 20

    v = (149 - 180.2) / 20

    v = (-31.2) / 20

    v = -1.56

    ### Answer: v = -1.56, x = 10.6

Expected answer: {v: 3202/1313, x: 7741/1313}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of t and g: 39 * t + 41 * g = 147 94 * t - 91 * g = 42.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of g's in both equations are the same:

    1) Multiply the first equation by 91:
    357t + 371g = 13257
    2) Multiply the second equation by 41:
    386t - 3731g = 1732

    Now, subtract the first equation from the second equation to eliminate the g term:

    (386t - 357t) - (371g - 371g) = 1732 - 13257
    29t = -11525

    Now, divide by 29:
    t = -11525/29
    t = -398

    Now that we have the value of t, substitute it into one of the original equations to find the value of g. We'll use the first equation:

    39t + 41g = 147
    39(-398) + 41g = 147
    -15342 + 41g = 147

    Add 15342 to both sides:
    41g = 15342 + 147
    41g = 15589

    Divide by 41:
    g = 15589/41
    g = 380

    ### Answer: t = -398, g = 380

Expected answer: {g: 12180/7403, t: 15099/7403}

Correct? No

🔗 Problem

Problem: Determine the values of c and o that satisfy the following system of equations: 6c + 55o = 112, and 55c - 48o = 36.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for c:

    c = (48o + 36) / 55

    Now, substitute this expression for c into the first equation:

    6((48o + 36) / 55) + 55o = 112

    Multiply both sides by 55 to eliminate the fraction:

    108o + 216 + 330o = 6160

    Combine like terms:

    438o = 5944

    Divide both sides by 438:

    o = 5944 / 438

    o = 13.5

    Now that we have found o, we can substitute this value back into one of the original equations to find c. We'll use the second equation:

    55c - 48(13.5) = 36

    55c - 648 = 36

    Add 648 to both sides:

    55c = 684

    Divide both sides by 55:

    c = 684 / 55

    c = 12.4

    So, the values of c and o that satisfy the system of equations are:

    c = 12.4
    o = 13.5

    ### Answer: c = 12.4, o = 13.5

Expected answer: {c: 7356/3313, o: 5944/3313}

Correct? No

🔗 Problem

Problem: Determine the values of u and w that satisfy the following system of equations: 8w + 68u = 170, 71w - 94u = 8.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for w:

    8w = 170 - 68u
    w = (170 - 68u) / 8

    Now, substitute this expression for w into the second equation:

    71((170 - 68u) / 8) - 94u = 8

    Multiply both sides by 8 to eliminate the fraction:

    71(170 - 68u) - 94u*8 = 8*8

    Expand and simplify:

    12170 - 4802u - 752u = 64

    Combine like terms:

    12170 - 5254u = 64

    Add 5254u to both sides:

    12170 = 64 + 5254u

    Subtract 64 from both sides:

    12106 = 5254u

    Divide both sides by 5254:

    u = 12106 / 5254
    u = 2.3

    Now that we have found u, we can substitute this value back into one of the original equations to find w. We'll use the first equation:

    8w + 68u = 170
    8w + 68(2.3) = 170

    Multiply 68 by 2.3:

    8w + 156.4 = 170

    Subtract 156.4 from both sides:

    8w = 13.6

    Divide both sides by 8:

    w = 13.6 / 8
    w = 1.7

    So, the values of u and w that satisfy the system of equations are:

    u = 2.3
    w = 1.7

    ### Answer: u = 2.3, w = 1.7

Expected answer: {u: 667/310, w: 459/155}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of r and f: 68*r + 8*f = 92 97*f + 38*r = 182

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of r's in both equations are the same:

    1) Multiply the first equation by 38:
    256*r + 304*f = 3508

    2) Multiply the second equation by 8:
    776*f + 304*r = 1456

    Now, subtract the first equation from the second equation to eliminate the r variable:

    776*f - 256*r = 1456 - 3508
    776*f - 256*r = -3262

    Now, add 256*r to both sides:

    776*f = -3262 + 256*r

    Now, divide both sides by 776:

    f = (-3262 + 256*r) / 776

    Now, substitute this expression for f into one of the original equations, say the first equation:

    68*r + 8*(-3262 + 256*r) = 92

    Expand and simplify:

    68*r - 26016 + 2048*r = 92

    Combine like terms:

    2116*r - 26016 = 92

    Add 26016 to both sides:

    2116*r = 26008

    Divide both sides by 2116:

    r = 26008 / 2116

    r = 12.25

    Now that we have the value of r, we can find the value of f by substituting r into the expression we found earlier:

    f = (-3262 + 256*12.25) / 776

    f = (-3262 + 3130) / 776

    f = 868 / 776

    f = 1.12

    ### Answer: r = 12.25, f = 1.12

Expected answer: {f: 2220/1573, r: 1867/1573}

Correct? No

🔗 Problem

Problem: Given the equations below, find the values of r and d: For the first equation, consider 67 apples, each worth d dollars, and 37 ragdolls, each worth r dollars. If the total value of all these items is $50, you can represent this situation with the equation 67d - 37r = 50. In another case, consider 39 ragdolls, each worth r dollars, and 21 apples, each worth d dollars. If the total value of all these items is $16, you can also represent this situation with the equation 39r - 21d = 16. From these two equations, find the values of d (the cost of each apple) and r (the cost of each ragdoll).

Llama 3 8B:

    Let's solve the system of equations.

    From the first equation, we have:

    67d - 37r = 50

    From the second equation, we have:

    39r - 21d = 16

    We can multiply the first equation by 21 and the second equation by 37 to make the coefficients of d equal:

    1437d - 1357r = 1070
    1439r - 777d = 592

    Now, we can subtract the second equation from the first equation to eliminate the r variable:

    -78d = 478

    Dividing both sides by -78, we get:

    d = -478/78
    d = -6.23

    Now that we have the value of d, we can substitute it into one of the original equations to find the value of r. Let's use the first equation:

    67d - 37r = 50
    67(-6.23) - 37r = 50
    -416.01 - 37r = 50

    Adding 416.01 to both sides:

    -37r = 466.01

    Dividing both sides by -37:

    r = 466.01/37
    r = 12.59

    ### Answer: d = -6.23, r = 12.59

Expected answer: {d: 1271/918, r: 1061/918}

Correct? No

🔗 Problem

Problem: To find the values of x and a, solve the following system of simultaneous linear equations: First equation: 163 equals 50 times x plus a Second equation: 24 equals 98 times x minus 84 times a.

Llama 3 8B:

    Let's solve the system of simultaneous linear equations.

    First equation: 163 = 50x + a

    Second equation: 24 = 98x - 84a

    We can solve this system by substituting the expression for a from the first equation into the second equation.

    Substitute a = 163 - 50x into the second equation:

    24 = 98x - 84(163 - 50x)

    Expand and simplify:

    24 = 98x - 13692 + 4200x
    24 = 4588x - 13692

    Add 13692 to both sides:

    13616 = 4588x

    Divide both sides by 4588:

    x = 13616/4588
    x = 3

    Now that we have found x, we can find a by substituting x into the first equation:

    163 = 50(3) + a
    163 = 150 + a

    Subtract 150 from both sides:

    13 = a

    So, the values of x and a are:

    x = 3
    a = 13

    ### Answer: x = 3, a = 13

Expected answer: {a: 7387/2149, x: 6858/2149}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of p and b: 67 * p + 18 * b = 110 82 * b - 44 * p = 58.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply both sides of the first equation by 44 to get:

    2952p + 792b = 4840

    Now, we can multiply both sides of the second equation by 67 to get:

    5494b - 2952p = 3866

    Now, we can add both equations to eliminate the p variable:

    5494b + 792b = 4840 + 3866
    6286b = 8716

    Now, we can divide both sides by 6286 to solve for b:

    b = 8716/6286
    b = 1.4

    Now that we have the value of b, we can substitute it into one of the original equations to solve for p. We'll use the first equation:

    67p + 18(1.4) = 110

    67p + 25.2 = 110

    Subtract 25.2 from both sides:

    67p = 84.8

    Divide both sides by 67:

    p = 84.8/67
    p = 1.26

    So, the values of p and b are:

    p = 1.26
    b = 1.4

    ### Answer: p = 1.26, b = 1.4

Expected answer: {b: 4363/3143, p: 3988/3143}

Correct? No

🔗 Problem

Problem: Determine the values of c and e from the following simultaneous equations: The difference between 63 times c and 36 times e equals 27, and 8 times c added to 32 times e equals 69.

Llama 3 8B:

    Let's solve the system of equations step by step.

    The first equation is:

    63c - 36e = 27

    The second equation is:

    8c + 32e = 69

    We can solve this system of equations by substitution or elimination. Let's use elimination.

    First, we can multiply the two equations by necessary multiples such that the coefficients of e's in both equations are the same:

    1) Multiply the first equation by 4:

    252c - 144e = 108

    2) Multiply the second equation by 3:

    24c + 96e = 207

    Now, subtract the first equation from the second equation to eliminate e:

    (24c + 96e) - (252c - 144e) = 207 - 108
    24c + 96e - 252c + 144e = 99
    -228c = 99

    Now, divide by -228:

    c = -99/228
    c = -27/76

    Now that we have the value of c, we can substitute it into one of the original equations to find the value of e. We'll use the first equation:

    63c - 36e = 27

    Substitute c = -27/76:

    63(-27/76) - 36e = 27

    Simplify:

    -1965/76 - 36e = 27

    Multiply both sides by -76 to eliminate the fraction:

    -1965 - 2736e = -76*27

    Add 1965 to both sides:

    -2736e = -1103

    Divide by -2736:

    e = 1103/2736
    e = 1103/2736

    ### Answer: c = -27/76, e = 1103/2736.

Expected answer: {c: 93/64, e: 459/256}

Correct? No

🔗 Problem

Problem: Solve the following system of linear equations to find the values of x and p: 26 * x + 29 * p = 107 61 * x - 51 * p = 4

Llama 3 8B:

    To solve this system of linear equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

    First, we will multiply both equations by necessary multiples such that the coefficients of p's in both equations are the same:

    1) Multiply the first equation by 51:
    51 * 26 * x + 51 * 29 * p = 51 * 107

    2) Multiply the second equation by 29:
    29 * 61 * x - 29 * 51 * p = 29 * 4

    Now, subtract the second equation from the first equation to eliminate p:

    (51 * 26 * x - 29 * 61 * x) + (51 * 29 * p - 29 * 51 * p) = 51 * 107 - 29 * 4

    Simplify the equation:

    23 * x = 51 * 107 - 29 * 4

    x = (51 * 107 - 29 * 4) / 23

    x = 53

    Now that we have the value of x, we can substitute it into one of the original equations to find the value of p. We will use the first equation:

    26 * x + 29 * p = 107

    26 * 53 + 29 * p = 107

    1378 + 29 * p = 107

    29 * p = -1271

    p = -1271 / 29

    p = -43.7

    ### Answer: x = 53, p = -43.7

Expected answer: {p: 6423/3095, x: 5573/3095}

Correct? No

🔗 Problem

Problem: Find the values for g and l from the system of equations below. The first equation is: ((29 * l) + (17 * g)) = 68. The second equation is: ((31 * g) - (10 * l)) = 17.

Llama 3 8B:

    Let's solve the system of equations step by step.

    From the second equation, we can express g in terms of l:

    g = (17 + 10l) / 31

    Now, substitute this expression for g into the first equation:

    ((29 * l) + (17 * ((17 + 10l) / 31))) = 68

    Simplify the equation:

    ((29 * l) + (17 * (17/31 + 10l/31))) = 68

    Combine like terms:

    ((29 * l) + (17 * 17/31) + (17 * 10l/31)) = 68

    Simplify further:

    (29l + 17 + 10l) = 68

    Combine like terms:

    39l + 17 = 68

    Subtract 17 from both sides:

    39l = 51

    Divide both sides by 39:

    l = 51/39

    l = 1.3077 (approximately)

    Now that we have the value of l, we can find the value of g:

    g = (17 + 10(1.3077)) / 31

    g ≈ 2.3459

    ### Answer: g ≈ 2.3459, l ≈ 1.3077.

Expected answer: {g: 1173/1069, l: 1819/1069}

Correct? No

🔗 Problem

Problem: Given the following system of equations, what are the values for a and c? 33*a - 54*c = 20 24*a - 26*c = 29.

Llama 3 8B:

    We can solve this system of equations by multiplying the two equations by necessary multiples such that the coefficients of c's in both equations are the same.

    First, multiply the first equation by 26 and the second equation by 54:

    104*a - 702*c = 520
    1312*a - 1428*c = 1581

    Now, subtract the first equation from the second equation to eliminate c:

    1208*a = 1061

    Now, divide by 1208:

    a = 1061/1208

    a = 0.88

    Now that we have the value of a, substitute it into one of the original equations to find the value of c. We'll use the first equation:

    33*a - 54*c = 20

    33*(0.88) - 54*c = 20

    33*0.88 - 54*c = 20

    29.04 - 54*c = 20

    Subtract 20 from both sides:

    29.04 - 54*c - 20 = 0

    -54*c = -9.04

    Divide by -54:

    c = 9.04/54

    c = 0.17

    ### Answer: a = 0.88, c = 0.17

Expected answer: {a: 523/219, c: 159/146}

Correct? No

🔗 Problem

Problem: Kat found herself stuck solving the following system of equations with two variables, d and j. Can you help her resolve it? 71d + 9j = 132 43j - 84d = 91.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of d's in both equations are the same:

    1) Multiply the first equation by 84:
    84(71d + 9j = 132) => 5884d + 756j = 11088

    2) Multiply the second equation by 1:
    43j - 84d = 91 => 43j - 84d = 91

    Now, we can subtract the second equation from the first equation to eliminate the d variable:

    (5884d + 756j = 11088) - (43j - 84d = 91)
    5884d + 756j - 43j + 84d = 11088 - 91
    5927d + 713j = 11097

    Now, we can solve for j:

    713j = 11097 - 5927d
    j = (11097 - 5927d) / 713

    Now that we have the expression for j, we can substitute it into one of the original equations to solve for d. Let's use the first equation:

    71d + 9j = 132
    71d + 9((11097 - 5927d) / 713) = 132

    Now, we can simplify the equation:

    71d + 9((11097 - 5927d) / 713) = 132
    71d + 9((11097 - 5927d) / 713) = 132
    71d + 9(11097 / 713 - 5927d / 713) = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132
    71d + 99 - 5927d / 713 = 132

Expected answer: {d: 4857/3809, j: 17549/3809}

Correct? No

🔗 Problem

Problem: Determine the values of o and n by solving this system of equations: (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for o:

    (81 * o) = 163 - (26 * n)
    o = (163 - (26 * n)) / 81

    Now, substitute this expression for o into the second equation:

    (87 * n) + (23 * ((163 - (26 * n)) / 81)) = 143

    Simplify the equation:

    (87 * n) + (23 * (163 - (26 * n))) / 81 = 143

    Multiply both sides by 81 to eliminate the fraction:

    (87 * n * 81) + (23 * (163 - (26 * n))) = 143 * 81

    Expand and simplify:

    7293n + 23(163 - 26n) = 11643

    Distribute the 23:

    7293n + 23(163) - 23(26n) = 11643

    Combine like terms:

    7293n + 3751 - 598n = 11643

    Combine the terms with n:

    5995n = 7902

    Divide both sides by 5995:

    n = 7902 / 5995

    n = 1.32

    Now that we have found n, we can substitute it back into one of the original equations to find o. We'll use the first equation:

    (81 * o) + (26 * 1.32) = 163

    (81 * o) + 34.32 = 163

    Subtract 34.32 from both sides:

    (81 * o) = 128.68

    Divide both sides by 81:

    o = 128.68 / 81

    o = 1.59

    So, the values of o and n are:

    o = 1.59
    n = 1.32

    ### Answer: o = 1.59, n = 1.32

Expected answer: {n: 7834/6449, o: 10463/6449}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for w and s: 46 * s - 61 * w = 2 61 * s + 67 * w = 178.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of w's in both equations are the same:

    1) Multiply the first equation by 67:
    67 * (46 * s - 61 * w) = 67 * 2
    2) Multiply the second equation by 61:
    61 * (61 * s + 67 * w) = 61 * 178

    Now, we can simplify and rewrite the equations:

    1) 67 * 46 * s - 67 * 61 * w = 134
    2) 61 * 61 * s + 61 * 67 * w = 10938

    Now, we can subtract the first equation from the second equation to eliminate w:

    (61 * 61 * s + 61 * 67 * w) - (67 * 46 * s - 67 * 61 * w) = 10938 - 134
    61 * 61 * s + 61 * 67 * w - 67 * 46 * s + 67 * 61 * w = 10904

    Combine like terms:

    (61 * 61 - 67 * 46) * s = 10904
    3721 * s = 10904

    Now, divide by 3721:

    s = 10904 / 3721
    s = 2.93

    Now that we have the value of s, we can substitute it into one of the original equations to find the value of w. We'll use the first equation:

    46 * s - 61 * w = 2
    46 * 2.93 - 61 * w = 2

    Simplify:

    135.78 - 61 * w = 2

    Subtract 135.78 from both sides:

    -61 * w = -133.78

    Divide by -61:

    w = 133.78 / 61
    w = 2.20

    So, the values of w and s are approximately 2.20 and 2.93, respectively.

    ### Answer: w ≈ 2.20, s ≈ 2.93.

Expected answer: {s: 10992/6803, w: 8066/6803}

Correct? No

🔗 Problem

Problem: In the following system of equations, calculate the values of i and k. System of equations: 51*k - 8*i = 86 39*i + 8*k = 193.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of i's in both equations are the same:

    1) Multiply the first equation by 39:
    195*k - 312*i = 3396
    2) Multiply the second equation by 51:
    1977*i + 408*k = 9843

    Now, subtract the first equation from the second equation to eliminate the i term:

    (1977*i - 195*k) + 408*k = 9843 - 3396
    1977*i + 213*k = 6447

    Now, we can solve for i:

    i = (6447 - 213*k) / 1977

    Now, substitute this expression for i into one of the original equations. We'll use the first equation:

    51*k - 8*((6447 - 213*k) / 1977) = 86

    Simplify the equation:

    51*k - 32.4 + 16.76*k = 86

    Combine like terms:

    67.76*k = 118.6

    Divide by 67.76:

    k = 1.75

    Now that we have the value of k, we can find the value of i:

    i = (6447 - 213*1.75) / 1977
    i = 6447 - 369.25
    i = 6077.75 / 1977
    i = 3.07

    ### Answer: i = 3.07, k = 1.75

Expected answer: {i: 9155/2053, k: 4898/2053}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of l and m: 26m + 17l = 146 93m + l = 126

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for l:

    l = 126 - 93m

    Now, substitute this expression for l into the first equation:

    26m + 17(126 - 93m) = 146

    Expand and simplify:

    26m + 2106 - 1593m = 146

    Combine like terms:

    -1567m = -1960

    Divide by -1567:

    m = 1960/1567

    m ≈ 1.25

    Now that we have found m, we can find l by substituting m back into one of the original equations. We'll use the second equation:

    l = 126 - 93(1.25)

    l = 126 - 116.25

    l ≈ 9.75

    So, the values of l and m are approximately:

    l ≈ 9.75
    m ≈ 1.25

    ### Answer: l ≈ 9.75, m ≈ 1.25

Expected answer: {l: 10302/1555, m: 1996/1555}

Correct? No

🔗 Problem

Problem: Determine the values of 'h' and 'f' by solving the following system of equations: 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119

Llama 3 8B:

    Let's solve the system of equations step by step.

    We have two equations:

    1) (8 * f) + (39 * h) = 66
    2) (29 * f) + (46 * h) = 119

    We can solve this system of equations using substitution or elimination. Let's use elimination.

    First, we can multiply equation (1) by 29 and equation (2) by 8 to make the coefficients of 'f' in both equations the same:

    29(1) => 232f + 1131h = 1914
    8(2) => 232f + 368h = 952

    Now, subtract equation (2) from equation (1) to eliminate 'f':

    (1914 - 952)h = 1914 - 952
    962h = 962

    Now, divide both sides by 962:

    h = 1

    Now that we have the value of 'h', we can substitute it into one of the original equations to find the value of 'f'. Let's use equation (1):

    (8 * f) + (39 * 1) = 66
    8f + 39 = 66

    Subtract 39 from both sides:

    8f = 27

    Divide both sides by 8:

    f = 27/8
    f = 3.375

    ### Answer: h = 1, f = 3.375

Expected answer: {f: 1605/763, h: 962/763}

Correct? No

🔗 Problem

Problem: Find the values of k and b that satisfy the following system of equations: 22 * b + 23 * k = 109 and 62 * k - 69 * b = 14.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for k:

    k = (109 - 22b) / 23

    Now, substitute this expression for k into the second equation:

    62((109 - 22b) / 23) - 69b = 14

    Multiply both sides by 23 to eliminate the fraction:

    1462 - 1032b - 1557b = 322

    Combine like terms:

    -2588b = -1140

    Divide both sides by -2588:

    b = 1140 / 2588

    b ≈ 0.44

    Now that we have found b, we can substitute it back into one of the original equations to find k. We'll use the first equation:

    22b + 23k = 109

    22(0.44) + 23k = 109

    9.68 + 23k = 109

    Subtract 9.68 from both sides:

    23k = 99.32

    Divide both sides by 23:

    k = 99.32 / 23

    k ≈ 4.31

    So, the values of k and b that satisfy the system of equations are:

    k ≈ 4.31
    b ≈ 0.44

    ### Answer: k ≈ 4.31, b ≈ 0.44.

Expected answer: {b: 6436/2951, k: 7829/2951}

Correct? No

🔗 Problem

Problem: Solve the following system of linear equations for the values of m and s: 1. 84m - 55s = 1 2. 63m - 2s = 98.

Llama 3 8B:

    Let's solve the system of linear equations step by step.

    First, we can multiply equation (2) by 2 to make the coefficients of s in both equations the same:

    2. 126m - 4s = 196

    Now we can subtract equation (1) from equation (2) to eliminate the s variable:

    (126m - 4s) - (84m - 55s) = 196 - 1
    42m + 51s = 195

    Next, we can multiply equation (1) by 63 to make the coefficients of m in both equations the same:

    1. 5292m - 3465s = 63

    Now we can subtract equation (1) from equation (2) to eliminate the m variable:

    (126m - 4s) - (5292m - 3465s) = 196 - 63
    -5166m + 3461s = 133

    Now we have a system of two equations with two variables:

    42m + 51s = 195
    -5166m + 3461s = 133

    We can solve this system using substitution or elimination. Let's use elimination. We can multiply equation (1) by 3461 and equation (2) by 51 to make the coefficients of s in both equations the same:

    1. 145422m - 178355s = 67815
    2. -26346m + 17531s = 8333

    Now we can subtract equation (1) from equation (2) to eliminate the s variable:

    (145422m - 178355s) - (-26346m + 17531s) = 67815 - 8333
    171768m = 49582

    Now we can solve for m:

    m = 49582 / 171768
    m = 0.288

    Now that we have the value of m, we can substitute it into one of the original equations to solve for s. Let's use equation (1):

    84m - 55s = 1
    84(0.288) - 55s = 1
    23.52 - 55s = 1

    Now we can solve for s:

    s = (1 - 23.52) / -55
    s = -22.52 / -55
    s = 0.408

    ### Answer: m = 0.288, s = 0.408

Expected answer: {m: 1796/1099, s: 389/157}

Correct? No

🔗 Problem

Problem: Given the following system of equations, find the values of b and k: 1. (6 * b) + (5 * k) = 105 2. (95 * k) - (51 * b) = 67.

Llama 3 8B:

    Let's solve the system of equations step by step.

    From the first equation, we can express b in terms of k:

    6b + 5k = 105
    6b = 105 - 5k
    b = (105 - 5k) / 6

    Now, substitute this expression for b into the second equation:

    95k - 51((105 - 5k) / 6) = 67

    Multiply both sides by 6 to eliminate the fraction:

    570k - 51(105 - 5k) = 402

    Expand and simplify:

    570k - 5335 + 255k = 402
    825k - 5335 = 402

    Add 5335 to both sides:

    825k = 6037

    Divide by 825:

    k = 6037 / 825
    k = 7.33

    Now that we have found k, we can find b by substituting k back into one of the original equations. We'll use the first equation:

    6b + 5k = 105
    6b + 5(7.33) = 105

    Multiply 5 by 7.33:

    6b + 36.65 = 105

    Subtract 36.65 from both sides:

    6b = 68.35

    Divide by 6:

    b = 68.35 / 6
    b = 11.39

    ### Answer: b = 11.39, k = 7.33

Expected answer: {b: 1928/165, k: 1919/275}

Correct? No

🔗 Problem

Problem: Determine the values of d and u from the following pair of simultaneous linear equations: 33d + 62u = 114 and 32u + 40d = 83.

Llama 3 8B:

    Let's solve the system of linear equations using substitution or elimination method.

    First, we can multiply the two equations by necessary multiples such that the coefficients of d's in both equations are the same:

    1) Multiply the first equation by 40 and the second equation by 62:

    1320d + 3860u = 4560
    1984u + 2480d = 5118

    2) Subtract the second equation from the first equation to eliminate d:

    1320d - 1984u = 4560 - 5118
    -1320d + 1984u = -5518

    3) Simplify the equation:

    -1320d + 1984u = -5518

    4) Now, we can solve for u:

    u = (-5518 + 1320d) / 1984

    5) Substitute the expression of u into one of the original equations, say the first equation:

    33d + 62(((-5518 + 1320d) / 1984)) = 114

    6) Simplify the equation:

    33d + 62((-5518 / 1984) + (1320d / 1984)) = 114

    7) Simplify further:

    33d - 5518/31 + 1320d/31 = 114

    8) Combine like terms:

    33d + 1320d/31 - 5518/31 = 114

    9) Simplify:

    (33 + 1320/31)d - 5518/31 = 114

    10) Add 5518/31 to both sides:

    (33 + 1320/31)d = 114 + 5518/31

    11) Simplify:

    (33 + 1320/31)d = 6326/31

    12) Multiply both sides by 31:

    (33 + 1320/31)d*31 = 6326/31*31

    13) Simplify:

    33d + 1320d = 6326

    14) Combine like terms:

    1353d = 6326

    15) Divide both sides by 1353:

    d = 6326/1353

    16) Now that we have the value of d, substitute it into the expression of u:

    u = (-5518 + 1320d) / 1984
    u = (-5518 + 1320(6326/1353)) / 1984
    u = (-5518 + 8328) / 1984
    u = 2810 / 1984

    17) Simplify:

    u = 1.42

    So, the values of d and u are:

    d = 6326/1353 ≈ 4.65
    u = 1.42

    ### Answer: d ≈ 4.65, u ≈ 1.42.

Expected answer: {d: 749/712, u: 1821/1424}

Correct? No

🔗 Problem

Problem: There are two equations below that contain the variables c and p. Can you solve this system of equations to find the values of c and p? 5 * c + 28 * p = 102 20 * c - 67 * p = 13

Llama 3 8B:

    Let's solve the system of equations.

    First, we can multiply the second equation by 5 to make the coefficients of p in both equations the same:

    100c - 335p = 65

    Now, we can add the two equations to eliminate the p variable:

    5c + 28p = 102
    100c - 335p = 65

    Adding the two equations, we get:

    105c = 167

    Now, we can solve for c:

    c = 167/105
    c = 1.57 (approximately)

    Now that we have the value of c, we can substitute it into one of the original equations to solve for p. We'll use the first equation:

    5c + 28p = 102

    Substituting c = 1.57, we get:

    5(1.57) + 28p = 102

    Simplifying, we get:

    7.85 + 28p = 102

    Subtracting 7.85 from both sides, we get:

    28p = 94.15

    Dividing both sides by 28, we get:

    p = 94.15/28
    p = 3.36 (approximately)

    ### Answer: c ≈ 1.57, p ≈ 3.36

Expected answer: {c: 7198/895, p: 395/179}

Correct? No

🔗 Problem

Problem: Given the following system of linear equations, determine the value of r and q. The system of equations is: 58 * r + 12 * q = 147 97 * q - 76 * r = 76.

Llama 3 8B:

    Let's solve the system of linear equations.

    We can start by multiplying the two equations by necessary multiples such that the coefficients of r's in both equations are the same:

    1) Multiply the first equation by 76:
    44r + 912q = 11208
    2) Multiply the second equation by 58:
    568q - 4484r = 4424

    Now, add both equations to eliminate the r term:

    (44r + 912q) + (568q - 4484r) = 11208 + 4424
    912q + 568q = 11208 + 4424
    1480q = 15632

    Now, divide by 1480:

    q = 15632/1480
    q = 10.53

    Now that we have the value of q, we can substitute it into one of the original equations to find the value of r. We'll use the first equation:

    58r + 12q = 147
    58r + 12(10.53) = 147
    58r + 126.36 = 147

    Subtract 126.36 from both sides:

    58r = 20.64

    Divide by 58:

    r = 20.64/58
    r = 0.357

    ### Answer: r = 0.357, q = 10.53

Expected answer: {q: 7790/3269, r: 13347/6538}

Correct? No

🔗 Problem

Problem: Resolve the provided system of simultaneous linear equations for v and k: 47 * v - 3 * k = 10 73 * v + 2 * k = 128.

Llama 3 8B:

    Let's solve the system of simultaneous linear equations.

    We have:

    1) 47v - 3k = 10 ... (Equation 1)
    2) 73v + 2k = 128 ... (Equation 2)

    We can solve this system using the method of substitution or elimination. Here, we'll use the elimination method.

    First, we'll multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of k in both equations the same:

    1) 94v - 6k = 20 ... (Equation 1 multiplied by 2)
    2) 219v + 6k = 384 ... (Equation 2 multiplied by 3)

    Now, we'll subtract Equation 1 from Equation 2 to eliminate k:

    (219v + 6k) - (94v - 6k) = 384 - 20
    225v = 364

    Now, we'll solve for v:

    v = 364/225
    v = 52/29
    v = 1.793 (approximately)

    Now that we have the value of v, we can substitute it into one of the original equations to find the value of k. We'll use Equation 1:

    47v - 3k = 10
    47(1.793) - 3k = 10
    83.531 - 3k = 10

    Now, we'll solve for k:

    -3k = -73.531
    k = 73.531/3
    k = 24.510 (approximately)

    So, the values of v and k are approximately 1.793 and 24.510, respectively.

    ### Answer: v ≈ 1.793, k ≈ 24.510.

Expected answer: {k: 5286/313, v: 404/313}

Correct? No

🔗 Problem

Problem: You are given the following system of equations: The result of 89 multiplied by p minus 41 multiplied by q equals 60. The result of 27 multiplied by p plus 91 multiplied by q equals 124. What are the values of p and q?

Llama 3 8B:

    Let's solve the system of equations.

    We have:

    1) 89p - 41q = 60
    2) 27p + 91q = 124

    We can solve this system of equations using substitution or elimination. Let's use elimination.

    First, we can multiply equation (1) by 41 and equation (2) by 89 to make the coefficients of q in both equations the same:

    1) 3647p - 1681q = 2460
    2) 2397p + 8039q = 10976

    Now, we can subtract equation (1) from equation (2) to eliminate q:

    2397p + 8039q - 3647p + 1681q = 10976 - 2460
    775p = 8426

    Now, we can solve for p:

    p = 8426/775
    p = 10.9

    Now that we have the value of p, we can substitute it into one of the original equations to solve for q. Let's use equation (1):

    89p - 41q = 60
    89(10.9) - 41q = 60
    969.1 - 41q = 60

    Now, we can solve for q:

    -41q = -909.1
    q = 909.1/41
    q = 22.2

    So, the values of p and q are:

    p = 10.9
    q = 22.2

    ### Answer: p = 10.9, q = 22.2

Expected answer: {p: 5272/4603, q: 4708/4603}

Correct? No

🔗 Problem

Problem: Find the values of u and d that make these equations true: The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71

Llama 3 8B:

    Let's solve the system of equations.

    From the first equation, we can express u in terms of d:

    u = (12 + 96d) / 88

    Now, substitute this expression for u into the second equation:

    (27((12 + 96d) / 88)) + (36d) = 71

    Simplify the equation:

    (27(12 + 96d) / 88) + 36d = 71

    Multiply both sides by 88 to eliminate the fraction:

    243 + 2592d + 3168d = 6232

    Combine like terms:

    4520d = 3989

    Divide both sides by 4520:

    d = 3989 / 4520

    d = 0.882

    Now that we have found d, we can find u:

    u = (12 + 96(0.882)) / 88

    u = (12 + 85.248) / 88

    u = 97.248 / 88

    u = 1.104

    ### Answer: u = 1.104, d = 0.882

Expected answer: {d: 1481/1440, u: 151/120}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of f and n: 20 * n - 18 * f = 9 and 3 * n - 2 * f = 70.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of f's in both equations are the same:

    1) Multiply the first equation by 2:
    40n - 36f = 18

    2) Multiply the second equation by 18:
    54n - 36f = 1260

    Now, subtract the first equation from the second equation to eliminate f:

    (54n - 40n) - (36f - 36f) = 1260 - 18
    14n = 1242

    Now, divide by 14:

    n = 1242/14
    n = 89

    Now that we have the value of n, substitute it into one of the original equations to find the value of f. We'll use the first equation:

    20n - 18f = 9
    20(89) - 18f = 9
    1780 - 18f = 9

    Subtract 1780 from both sides:

    -18f = -1771
    f = 1771/(-18)
    f = -98.5

    ### Answer: f = -98.5, n = 89.

Expected answer: {f: 1373/14, n: 621/7}

Correct? No

🔗 Problem

Problem: Determine the values of j and l from the following system of equations: 7 * l + 97 * j = 133 22 * j + 37 * l = 76.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for l:

    l = (133 - 97j) / 7

    Now, substitute this expression for l into the second equation:

    22j + 37((133 - 97j) / 7) = 76

    Multiply both sides of the equation by 7 to eliminate the fraction:

    154j + 37(133 - 97j) = 532

    Expand and simplify the equation:

    154j + 4933 - 3577j = 532

    Combine like terms:

    -2103j = -4401

    Divide both sides by -2103:

    j = 4401 / 2103

    j = 2

    Now that we have found j, we can find l by substituting j into one of the original equations. We'll use the first equation:

    7l + 97(2) = 133

    7l + 194 = 133

    Subtract 194 from both sides:

    7l = -61

    Divide both sides by 7:

    l = -61/7

    l = -8.71 (rounded to two decimal places)

    ### Answer: j = 2, l = -8.71.

Expected answer: {j: 1463/1145, l: 1482/1145}

Correct? No

🔗 Problem

Problem: Determine the values of d and f from the following system of equations: 21d - 46f = 53 8d + 84f = 133.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of f's in both equations are the same:

    1) Multiply the first equation by 84:
    168d - 3884f = 4428
    2) Multiply the second equation by 46:
    368d + 3864f = 6118

    Now, subtract the first equation from the second equation to eliminate f:

    (368d + 3864f) - (168d - 3884f) = 6118 - 4428
    368d + 3864f - 168d + 3884f = 6118 - 4428
    200d + 7748f = 1690

    Now, divide both sides by 200:

    d + 38.74f = 8.45

    Now, substitute this expression for d into one of the original equations. We'll use the first equation:

    21d - 46f = 53
    21(d + 38.74f) - 46f = 53
    21(8.45) - 46f = 53
    177.45 - 46f = 53

    Now, subtract 53 from both sides:

    177.45 - 46f - 53 = 0
    -46f = -25.55

    Now, divide both sides by -46:

    f = 25.55/46
    f = 0.55

    Now that we have found f, we can substitute it back into the expression for d:

    d + 38.74f = 8.45
    d + 38.74(0.55) = 8.45
    d + 21.29 = 8.45
    d = 8.45 - 21.29
    d = -12.84

    ### Answer: d = -12.84, f = 0.55

Expected answer: {d: 5285/1066, f: 2369/2132}

Correct? No

🔗 Problem

Problem: Determine the values of u and w that satisfy the following system of equations: 74u + 11w = 116 66u - 68w = 21.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of w's in both equations are the same:

    1) Multiply the first equation by 68 and the second equation by 11:

    476u + 748w = 7936
    726u - 748w = 231

    2) Now, add both equations to eliminate w:

    1102u = 8167

    3) Divide by 1102:

    u = 8167/1102
    u = 7.4

    4) Now that we have the value of u, substitute it into one of the original equations to find the value of w. We'll use the first equation:

    74u + 11w = 116
    74(7.4) + 11w = 116
    551 + 11w = 116

    5) Subtract 551 from both sides:

    11w = -435

    6) Divide by 11:

    w = -435/11
    w = -39.5

    So, the values of u and w that satisfy the system of equations are:

    u = 7.4
    w = -39.5

    ### Answer: u = 7.4, w = -39.5

Expected answer: {u: 8119/5758, w: 3051/2879}

Correct? No

🔗 Problem

Problem: Find the values of f and j that will satisfy the following system of equations: 76 * f - 42 * j = 96 47 * j + 34 * f = 136.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for f:

    76f - 42j = 96
    76f = 96 + 42j
    f = (96 + 42j) / 76

    Now, substitute this expression for f into the second equation:

    47j + 34((96 + 42j) / 76) = 136

    Multiply both sides by 76 to eliminate the fraction:

    2827j + 2856 + 1272j = 10304

    Combine like terms:

    2549j = 7468

    Divide both sides by 2549:

    j = 7468 / 2549
    j = 2.93 (approximately)

    Now that we have found j, we can substitute it back into one of the original equations to find f. We'll use the first equation:

    76f - 42(2.93) = 96

    Simplify:

    76f - 124.86 = 96

    Add 124.86 to both sides:

    76f = 220.86

    Divide both sides by 76:

    f = 220.86 / 76
    f = 2.91 (approximately)

    ### Answer: f ≈ 2.91, j ≈ 2.93.

Expected answer: {f: 1278/625, j: 884/625}

Correct? No

🔗 Problem

Problem: Consider the following system of equations. Find the values of u and e: 68u + 32e = 174 63e - 69u = 1.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for e:

    e = (1 + 69u) / 63

    Now, substitute this expression for e into the first equation:

    68u + 32((1 + 69u) / 63) = 174

    Multiply both sides by 63 to eliminate the fraction:

    4256u + 2048 = 10872

    Subtract 2048 from both sides:

    4256u = 8824

    Divide both sides by 4256:

    u = 8824 / 4256

    u = 2

    Now that we have found u, we can find e by substituting u back into one of the original equations. We'll use the second equation:

    e = (1 + 69(2)) / 63

    e = (1 + 138) / 63

    e = 139 / 63

    e = 13/7

    ### Answer: u = 2, e = 13/7

Expected answer: {e: 6037/3246, u: 5465/3246}

Correct? No

🔗 Problem

Problem: Find the values of p and n that satisfy the following system of linear equations: 57p + 4n = 129 and 24p + 39n = 154.

Llama 3 8B:

    We can solve this system of linear equations using the method of substitution or elimination. Here, we will use the elimination method.

    First, we will multiply the two equations by necessary multiples such that the coefficients of n's in both equations are the same:

    1) Multiply the first equation by 39 and the second equation by 4:

    195p + 156n = 5013
    96p + 156n = 616

    Now, subtract the second equation from the first equation to eliminate n:

    195p - 96p = 5013 - 616
    99p = 4397

    Now, divide by 99:

    p = 4397/99
    p = 44

    Now that we have the value of p, substitute it in one of the original equations to find the value of n. We will use the first equation:

    57p + 4n = 129
    57(44) + 4n = 129
    2512 + 4n = 129

    Subtract 2512 from both sides:

    4n = -2383
    n = -2383/4
    n = -599.25

    ### Answer: p = 44, n = -599.25

Expected answer: {n: 1894/709, p: 4415/2127}

Correct? No

🔗 Problem

Problem: Determine the values of y and z from the given system of equations: 66 * z - 44 * y = 32 60 * y + 14 * z = 116.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for y:

    60y + 14z = 116
    60y = 116 - 14z
    y = (116 - 14z) / 60

    Now, substitute this expression for y into the first equation:

    66z - 44((116 - 14z) / 60) = 32

    Multiply both sides by 60 to eliminate the fraction:

    3960z - 2640(116 - 14z) = 1920

    Expand and simplify:

    3960z - 307200 + 37120z = 1920
    46780z = 308320

    Divide both sides by 46780:

    z = 308320 / 46780
    z = 6.6

    Now that we have found z, we can substitute it back into one of the original equations to find y. We'll use the second equation:

    60y + 14(6.6) = 116

    60y + 92.4 = 116

    Subtract 92.4 from both sides:

    60y = 23.6

    Divide both sides by 60:

    y = 23.6 / 60
    y = 0.39

    ### Answer: y = 0.39, z = 6.6

Expected answer: {y: 901/572, z: 439/286}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the variables t and h: The first equation is 83 * t - 58 * h = 45. The second equation is 69 * h + 11 * t = 124.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply both sides of the first equation by 58 to get:

    83t = 45 + 58h

    Next, we can multiply both sides of the second equation by 11 to get:

    769h + 121t = 1374

    Now, we can subtract the first equation from the second equation to eliminate the h variable:

    769h - 83t = 1374 - 45
    = 1329

    Now, we can divide both sides by 83 to get:

    h = (1329 - 83t) / 769

    Now, we can substitute this expression for h into one of the original equations. Let's use the first equation:

    83t - 58((1329 - 83t) / 769) = 45

    To simplify this equation, we can multiply both sides by 769 to get rid of the fraction:

    61957 - 9764t = 34965

    Next, we can subtract 34965 from both sides to get:

    -26992 = -9764t

    Finally, we can divide both sides by -9764 to solve for t:

    t = 26992 / 9764
    = 2.77

    Now that we have found t, we can substitute this value back into one of the original equations to find h. Let's use the second equation:

    69h + 11(2.77) = 124

    To solve for h, we can subtract 30.67 from both sides:

    69h = 93.33

    Finally, we can divide both sides by 69 to solve for h:

    h = 93.33 / 69
    = 1.35

    ### Answer: t = 2.77, h = 1.35

Expected answer: {h: 9797/6365, t: 10297/6365}

Correct? No

🔗 Problem

Problem: Given the system of equations ((79 * h) - (61 * o)) = 9 and ((16 * h) - (12 * o)) = 9, what are the values of o and h?

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for h:

    h = (12 * o + 9) / 16

    Now, substitute this expression for h into the first equation:

    (79 * ((12 * o + 9) / 16)) - (61 * o) = 9

    Simplify the equation:

    (946.5 * o + 693) - 61 * o = 9

    Combine like terms:

    885.5 * o = -684

    Divide both sides by 885.5:

    o = -684 / 885.5

    o ≈ -0.77

    Now that we have the value of o, substitute it back into the expression for h:

    h = (12 * (-0.77) + 9) / 16

    h = (-9.24 + 9) / 16

    h = 0.76 / 16

    h ≈ 0.0475

    So, the values of o and h are approximately o ≈ -0.77 and h ≈ 0.0475.

    ### Answer: o ≈ -0.77, h ≈ 0.0475.

Expected answer: {h: 63/4, o: 81/4}

Correct? No

🔗 Problem

Problem: Solve for variables s and y when the following system of equations is satisfied: 4 * y + 56 * s = 139 65 * y - 90 * s = 16

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for s:

    s = (139 - 4y) / 56

    Now, substitute this expression for s into the second equation:

    65y - 90((139 - 4y) / 56) = 16

    Multiply both sides by 56 to eliminate the fraction:

    65y - 90(139 - 4y) = 16 * 56

    Expand and simplify:

    65y - 12570 + 360y = 896

    Combine like terms:

    425y = 12590

    Divide by 425:

    y = 12590 / 425

    y = 29.5

    Now that we have found y, substitute it back into one of the original equations to find s. We'll use the first equation:

    4 * 29.5 + 56 * s = 139

    Expand and simplify:

    117 + 56s = 139

    Subtract 117 from both sides:

    56s = 22

    Divide by 56:

    s = 22 / 56

    s = 0.4

    ### Answer: s = 0.4, y = 29.5

Expected answer: {s: 8971/4000, y: 6703/2000}

Correct? No

🔗 Problem

Problem: Solve the following pair of simultaneous equations: 42 * d - 4 * z = 75 40 * d + 45 * z = 162 Find the values of d and z.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of z's in both equations are the same:

    1) Multiply the first equation by 45:
    1825d - 180z = 3375
    2) Multiply the second equation by 4:
    160d + 180z = 648

    Now, subtract the first equation from the second equation to eliminate z:

    (160d + 180z) - (1825d - 180z) = 648 - 3375
    160d - 1825d = 648 - 3375
    -1665d = -2727
    d = 2727/1665
    d = 1.64

    Now that we have the value of d, we can substitute it into one of the original equations to find the value of z. We'll use the first equation:

    42d - 4z = 75
    42(1.64) - 4z = 75
    67.68 - 4z = 75
    -4z = 75 - 67.68
    -4z = 7.32
    z = -7.32/4
    z = -1.83

    ### Answer: d = 1.64, z = -1.83

Expected answer: {d: 4023/2050, z: 1902/1025}

Correct? No

🔗 Problem

Problem: Determine the values of 'a' and 'o' from the following system of equations: (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for 'a':

    (42 * a) + (6 * o) = 75
    42 * a = 75 - 6 * o
    a = (75 - 6 * o) / 42

    Now, substitute this expression for 'a' into the first equation:

    (42 * o) + (24 * ((75 - 6 * o) / 42)) = 142

    Simplify the equation:

    42 * o + 24 * ((75 - 6 * o) / 42) = 142
    42 * o + 24 * (75 / 42 - 6 * o / 42) = 142
    42 * o + 24 * (75 / 42) - 24 * 6 * o / 42 = 142
    42 * o + 18 - 24 * 6 * o / 42 = 142
    42 * o + 18 - 12 * o = 142
    30 * o + 18 = 142
    30 * o = 142 - 18
    30 * o = 124
    o = 124 / 30
    o = 4

    Now that we have the value of 'o', we can substitute it back into one of the original equations to find the value of 'a'. We'll use the second equation:

    (42 * a) + (6 * 4) = 75
    42 * a + 24 = 75
    42 * a = 75 - 24
    42 * a = 51
    a = 51 / 42
    a = 1.21

    So, the values of 'a' and 'o' are approximately 1.21 and 4, respectively.

    ### Answer: a ≈ 1.21, o ≈ 4.

Expected answer: {a: 383/270, o: 347/135}

Correct? No

🔗 Problem

Problem: Given the following system of equations, find the values of p and r: 39*r - 2*p = 45 and 16*p - 84*r = 36.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of r's in both equations are the same:

    1) Multiply the first equation by 16 and the second equation by 2:

    624*r - 32*p = 720 and 32*p - 168*r = 72

    Now, we can subtract the second equation from the first equation to eliminate the term with r:

    624*r - 32*p - (32*p - 168*r) = 720 - 72

    This simplifies to:

    792*r = 648

    Now, divide both sides by 792:

    r = 648/792

    r = 3/4

    Now that we have the value of r, we can substitute it into one of the original equations to find the value of p. We'll use the first equation:

    39*(3/4) - 2*p = 45

    Simplify the left-hand side:

    29.25 - 2*p = 45

    Subtract 29.25 from both sides:

    -2*p = 15.75

    Divide both sides by -2:

    p = -15.75/2

    p = -7.875

    ### Answer: p = -7.875, r = 3/4.

Expected answer: {p: 216/19, r: 33/19}

Correct? No

🔗 Problem

Problem: Given the following system of equations, solve for the values of 'd' and 'w': 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58

Llama 3 8B:

    Let's solve the system of equations step by step.

    From equation (1), we can express 'd' in terms of 'w':

    d = (7 + 52w) / 23

    Now, substitute this expression for 'd' into equation (2):

    (64w) - (8 * ((7 + 52w) / 23)) = 58

    Simplify the equation:

    64w - (56/23) - (416w/23) = 58

    Combine like terms:

    (48w - 56/23) = 58

    Multiply both sides by 23 to eliminate the fraction:

    1080w - 56 = 1318

    Add 56 to both sides:

    1080w = 1374

    Divide both sides by 1080:

    w = 1374/1080

    w = 1.275

    Now that we have the value of 'w', we can find the value of 'd':

    d = (7 + 52(1.275)) / 23

    d = (7 + 65.5) / 23

    d = 72.5 / 23

    d = 3.15

    ### Answer: d = 3.15, w = 1.275

Expected answer: {d: 433/132, w: 695/528}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of n and z: (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can multiply the two equations by necessary multiples such that the coefficients of n's in both equations are the same:

    1) Multiply the first equation by 47:
    47(71z + 60n) = 47(184)
    2) Multiply the second equation by 60:
    60(52z - 47n) = 60(19)

    Now, we can subtract the second equation from the first equation:

    47(71z + 60n) - 60(52z - 47n) = 47(184) - 60(19)
    47(71z + 60n) - 60(52z - 47n) = 862 - 1140
    47(71z + 60n) - 60(52z - 47n) = -278

    Now, simplify the equation:

    47(71z) + 47(60n) - 60(52z) + 60(47n) = -278
    47(71z) - 60(52z) + 47(60n) + 60(47n) = -278
    7z - 60z + 2820 + 2820 = -278
    -53z + 5640 = -278

    Now, add 278 to both sides:

    -53z + 5640 = 0
    -53z = -5640

    Now, divide both sides by -53:

    z = 5640/53
    z = 106

    Now that we have the value of z, we can substitute it into one of the original equations to find the value of n. We'll use the first equation:

    71z + 60n = 184
    71(106) + 60n = 184
    7540 + 60n = 184

    Now, subtract 7540 from both sides:

    60n = -7356
    n = -7356/60
    n = -123

    ### Answer: n = -123, z = 106.

Expected answer: {n: 8219/6457, z: 9788/6457}

Correct? No

🔗 Problem

Problem: Given the following system of equations, find the values of e and z: 70 * e + 90 * z = 189 99 * z - 84 * e = 20

Llama 3 8B:

    Let's solve the system of equations using the method of substitution or elimination.

    First, let's multiply both equations by necessary multiples such that the coefficients of e's in both equations are the same:

    1) Multiply the first equation by 84:
    588e + 756z = 1584
    2) Multiply the second equation by 70:
    693z - 588e = 1400

    Now, subtract the first equation from the second equation to eliminate e:

    693z - 588e - (588e + 756z) = 1400 - 1584
    693z - 588e - 588e - 756z = -84
    -1053e = -84

    Now, divide both sides by -1053:

    e = 84/1053
    e = 8/103

    Now that we have the value of e, substitute it into one of the original equations to find the value of z. We'll use the first equation:

    70e + 90z = 189
    70(8/103) + 90z = 189

    Multiply both sides by 103:

    560 + 90z = 19383
    90z = 19323
    z = 19323/90
    z = 214

    ### Answer: e = 8/103, z = 214

Expected answer: {e: 1879/1610, z: 1234/1035}

Correct? No

🔗 Problem

Problem: Find the values of o and f that satisfy the following system of equations: 1) 26o - 44f = 95 2) 87f + 11o = 169.

Llama 3 8B:

    Let's solve the system of equations step by step.

    From equation (1), we can express o in terms of f:

    o = (95 + 44f) / 26

    Now, substitute this expression for o into equation (2):

    87f + 11((95 + 44f) / 26) = 169

    Multiply both sides by 26 to eliminate the fraction:

    2197f + 1215 + 121f = 4366

    Combine like terms:

    2318f + 1215 = 4366

    Subtract 1215 from both sides:

    2318f = 3151

    Divide both sides by 2318:

    f = 3151 / 2318

    f = 1.36 (approximately)

    Now that we have found f, we can find o by substituting f back into the expression we found earlier:

    o = (95 + 44(1.36)) / 26

    o = (95 + 59.84) / 26

    o = 154.84 / 26

    o = 5.96 (approximately)

    ### Answer: o ≈ 5.96, f ≈ 1.36.

Expected answer: {f: 3349/2746, o: 15701/2746}

Correct? No

🔗 Problem

Problem: Calculate the values of z and p using the following system of equations: 40*z - 20*p = 51 6*z + 58*p = 165.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the first equation for z:

    40*z - 20*p = 51
    40*z = 51 + 20*p
    z = (51 + 20*p) / 40

    Now, substitute this expression for z into the second equation:

    6*(51 + 20*p) / 40 + 58*p = 165

    Multiply both sides by 40 to eliminate the fraction:

    6*(51 + 20*p) + 58*p*40 = 165*40

    Expand and simplify:

    306 + 120*p + 2320*p = 6600

    Combine like terms:

    2446*p = 6294

    Divide by 2446:

    p = 6294 / 2446
    p = 2.57 (approximately)

    Now that we have found p, we can substitute it back into one of the original equations to find z. We'll use the first equation:

    40*z - 20*p = 51
    40*z - 20*2.57 = 51

    Add 102.8 to both sides:

    40*z = 153.8

    Divide by 40:

    z = 153.8 / 40
    z = 3.845 (approximately)

    ### Answer: z ≈ 3.845, p ≈ 2.57.

Expected answer: {p: 3147/1220, z: 3129/1220}

Correct? No

🔗 Problem

Problem: Find the values of s and f from the given system of equations: (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93.

Llama 3 8B:

    Let's solve the system of equations step by step.

    First, we can solve the second equation for f:

    3f + 10s = 93
    3f = 93 - 10s
    f = (93 - 10s) / 3

    Now, substitute this expression for f into the first equation:

    (71s) - (89((93 - 10s) / 3)) = 5

    Multiply both sides by 3 to eliminate the fraction:

    213s - 267(93 - 10s) = 15

    Expand and simplify:

    213s - 24837 + 2670s = 15

    Combine like terms:

    1483s = 24952

    Divide both sides by 1483:

    s = 24952 / 1483
    s = 16.8

    Now that we have the value of s, we can find the value of f:

    f = (93 - 10(16.8)) / 3
    f = (93 - 168) / 3
    f = -75 / 3
    f = -25

    ### Answer: s = 16.8, f = -25

Expected answer: {f: 6553/1103, s: 8292/1103}

Correct? No