Solve the following system of equations for all three variables.

5x-2y+z = 8

-9x+2y+2z = 5

-9x-2y-5z = 4

5x - 2y + 1z = 8 ⇒ 5x - 2y + 1z = 8

-9x + 2y + 2z = 5 ⇒ - 9x + 2y + 2z = 5

-9x - 2y - 5z = 4 - 4x + 3z = 13

5x - 2y + 1z = 8

-9x + 2y + 2z = 5 ⇒ - 9x + 2y + 2z = 5

-9z - 2y - 5z = 4 ⇒ - 9x - 2y - 5z = 4

-18x - 3z = 9

-4x + 3z = 13

-18x - 3z = 9

-22x = 22

-22 - 22

x = - 1

-18x - 3z = 9

-18 (-1) - 3z = 9

18 - 3z = 9

- 18 - 18

-3z = - 9

-3 - 3

z = 3

5x - 2y + z = 8

5 (-1) - 2y + 3 = 8

-5 - 2y + 3 = 8

-2y - 5 + 3 = 8

-2y - 2 = 8

+ 2 + 2

-2y = 10

-2 - 2

y = - 5

(x, y, z) = (-1, - 5, 3)