Solve each system of equations (systems with 3 variables)

9x + 3y - 4z = 37

4x + 3y + 7z = 16

x - 5y + 8z = - 31

my answer is (2,5,-1)

is that right?

x = 2, y = 5, z = - 1 You are correct!

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:

Answer: {x = 2, y = 5, z = - 1