What is the solution to the following system 4x+3y-z=-6

Solve equation [2] for the variable y

[2] y = 6x + 3z - 12

/ / Plug this in for variable y in equation [1]

[1] 4x + 3• (6x+3z-12) - z = - 6 [1] 22x + 8z = 30

/ / Plug this in for variable y in equation [3]

[3] 8x + 2• (6x+3z-12) + 4z = 6 [3] 20x + 10z = 30

/ / Solve equation [3] for the variable z

[3] 10z = - 20x + 30 [3] z = - 2x + 3

/ / Plug this in for variable z in equation [1]

[1] 22x + 8• (-2x+3) = 30 [1] 6x = 6

/ / Solve equation [1] for the variable x

[1] 6x = 6 [1] x = 1

/ / By now we know this much:

x = 1 y = 6x+3z-12 z = - 2x+3

/ / Use the x value to solve for z

z = - 2 (1) + 3 = 1

/ / Use the x and z values to solve for y

y = 6 (1) + 3 (1) - 12 = - 3

Solution : {x, y, z} = {1,-3,1}