9x+3y-4z=37
4x+3y +7z =16
x-5y +8z=-31

x = 2 , y = 5 , z = -1

Step-by-step explanation:

Solve the following system:

{9 x + 3 y - 4 z = 37 | (equation 1)

4 x + 3 y + 7 z = 16 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 4/9 × (equation 1) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+(5 y)/3 + (79 z)/9 = -4/9 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Multiply equation 2 by 9:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 1/9 × (equation 1) from equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - (16 y)/3 + (76 z)/9 = -316/9 | (equation 3)

Multiply equation 3 by 9/4:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - 12 y + 19 z = -79 | (equation 3)

Add 4/5 × (equation 2) to equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+(411 z)/5 = -411/5 | (equation 3)

Multiply equation 3 by 5/411:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 79 × (equation 3) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y+0 z = 75 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 2 by 15:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 3 × (equation 2) from equation 1:

{9 x + 0 y - 4 z = 22 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Add 4 × (equation 3) to equation 1:

{9 x+0 y+0 z = 18 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 1 by 9:

{x+0 y+0 z = 2 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Collect results:

 {x = 2 , y = 5 , z = -1