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If a + b = -8 , and b + c = 3, and a + c = 5. Then what is a times b times c ?

 Aug 10, 2020
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Solve the following system:
{a + b = -8 | (equation 1)
b + c = 3 | (equation 2)
a + c = 5 | (equation 3)

Subtract equation 1 from equation 3:
{a + b+0 c = -8 | (equation 1)
0 a+b + c = 3 | (equation 2)
0 a - b + c = 13 | (equation 3)

Add equation 2 to equation 3:
{a + b+0 c = -8 | (equation 1)
0 a+b + c = 3 | (equation 2)
0 a+0 b+2 c = 16 | (equation 3)

Divide equation 3 by 2:
{a + b+0 c = -8 | (equation 1)
0 a+b + c = 3 | (equation 2)
0 a+0 b+c = 8 | (equation 3)

Subtract equation 3 from equation 2:
{a + b+0 c = -8 | (equation 1)
0 a+b+0 c = -5 | (equation 2)
0 a+0 b+c = 8 | (equation 3)

Subtract equation 2 from equation 1:
{a+0 b+0 c = -3 | (equation 1)
0 a+b+0 c = -5 | (equation 2)
0 a+0 b+c = 8 | (equation 3)

Collect results:
a = -3,      b = -5,      c = 8    =-3   x    - 5    x      8 == 120

 Aug 10, 2020

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