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