Okay, let's see. I need to find the product abc given these three equations: a + b = 8, b + c = -3, and a + c = -5. Hmm, so there are three variables and three equations. That should be solvable by substitution or elimination. Let me think about how to approach this.

First, maybe I can express each variable in terms of another and substitute. Let me write down the equations again:

1. a + b = 8
2. b + c = -3
3. a + c = -5

Hmm, if I subtract equation 2 from equation 1, maybe that will help. Let's try that.

Equation 1 minus equation 2: (a + b) - (b + c) = 8 - (-3). Simplifying the left side: a + b - b - c = a - c. The right side: 8 + 3 = 11. So, a - c = 11.

But wait, equation 3 is a + c = -5. So now I have two equations involving a and c:

a - c = 11
a + c = -5

If I add these two equations together, the c terms will cancel out. Let's do that:

(a - c) + (a + c) = 11 + (-5)
2a = 6
So, a = 3.

Now that I have a = 3, I can substitute back into equation 3 to find c. Equation 3 is a + c = -5, so 3 + c = -5. Subtracting 3 from both sides gives c = -8.

Now that I have a and c, I can find b using equation 1. Equation 1 is a + b = 8. Since a is 3, 3 + b = 8. Subtracting 3 gives b = 5.

Wait, let me check if these values satisfy all equations. Let's verify:

1. a + b = 3 + 5 = 8 ✔️
2. b + c = 5 + (-8) = -3 ✔️
3. a + c = 3 + (-8) = -5 ✔️

All equations check out. So the values are a = 3, b = 5, c = -8. Therefore, the product abc is 3 * 5 * (-8). Let's compute that.

3 * 5 is 15, and 15 * (-8) is -120. So the product abc is -120.

Wait, but let me make sure I didn't make a mistake in the algebra. Let me go through the steps again.

Starting with the three equations:

1. a + b = 8
2. b + c = -3
3. a + c = -5

Subtracting equation 2 from equation 1: a - c = 11. Then adding that to equation 3: a - c + a + c = 11 + (-5) => 2a = 6 => a = 3. Then c = a + c - a = (-5) - 3 = -8. Then b = 8 - a = 8 - 3 = 5. Correct.

Therefore, the product is 3 * 5 * (-8) = -120. Yeah, that seems right. I don't see any errors here. So the answer should be -120.
Therefore, the value of the product $abc$ is $\boxed{-120}$.
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