2x+3y-2z=8

3x-y+4z=-20

x+y-z=3

Take the 3rd equation and multiply by 2 to get

2x + 2y - 2z = 6

Subtract from 1st equation to get

y = 2

Substitute into all equations

2x + 3(2) - 2z = 8

2x - 2z = 2

3x - 2 + 4z = -20

3x + 4z = -18

x + 2 - z = 3

x - z = 1 Multiply by 4 and add to 3x + 4z = -18 to get

7x = -14

x = -2

and finally plug into original 3rd equation

(-2) + 2 - z = 3

-z = 3

z = - 3

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