\(\begin{align*} x+y-z &= -8, \\ x-y+z &= 18,\text{ and} \\ -x+y+z &= 30, \\ \end{align*}\)

Guest Nov 30, 2020

#2**+1 **

Solve the following system:

{x + y - z = -8 | (equation 1)

x - y + z = 18 | (equation 2)

-x + y + z = 30 | (equation 3)

Subtract equation 1 from equation 2:

{x + y - z = -8 | (equation 1)

0 x - 2 y + 2 z = 26 | (equation 2)

-x + y + z = 30 | (equation 3)

Divide equation 2 by 2:

{x + y - z = -8 | (equation 1)

0 x - y + z = 13 | (equation 2)

-x + y + z = 30 | (equation 3)

Add equation 1 to equation 3:

{x + y - z = -8 | (equation 1)

0 x - y + z = 13 | (equation 2)

0 x+2 y+0 z = 22 | (equation 3)

Divide equation 3 by 2:

{x + y - z = -8 | (equation 1)

0 x - y + z = 13 | (equation 2)

0 x+y+0 z = 11 | (equation 3)

Add equation 2 to equation 3:

{x + y - z = -8 | (equation 1)

0 x - y + z = 13 | (equation 2)

0 x+0 y+z = 24 | (equation 3)

Subtract equation 3 from equation 2:

{x + y - z = -8 | (equation 1)

0 x - y+0 z = -11 | (equation 2)

0 x+0 y+z = 24 | (equation 3)

Multiply equation 2 by -1:

{x + y - z = -8 | (equation 1)

0 x+y+0 z = 11 | (equation 2)

0 x+0 y+z = 24 | (equation 3)

Subtract equation 2 from equation 1:

{x + 0 y - z = -19 | (equation 1)

0 x+y+0 z = 11 | (equation 2)

0 x+0 y+z = 24 | (equation 3)

Add equation 3 to equation 1:

{x+0 y+0 z = 5 | (equation 1)

0 x+y+0 z = 11 | (equation 2)

0 x+0 y+z = 24 | (equation 3)

**x = 5, y = 11, z = 24 xyz =5 x 11 x 24 =1,320**

Guest Nov 30, 2020