Answer
$x=0$
$y=8$
$z=-5$
Work Step by Step
Using elimination for the first two equations:
$4x-y+2z=-18$
$-x+2y+z=11$
Multiply both sides of the second equation by $4$:
$4x-y+2z=-18$
$-4x+8y+4z=44$
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$7y+6z=26$ (1)
Using elimination for the second and the third equations:
$-x+2y+z=11$
$3x+3y-4z=44$
Multiply both sides of the first equation by $3$:
$-3x+6y+3z=33$
$3x+3y-4z=44$
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$9y-z=77$ (2)
From (1) and (2):
$7y+6z=26$
$9y-z=77$
Multiply both sides of the second equation by $6$:
$7y+6z=26$
$54y-6z=462$
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$61y=488$
$y=8$
Solve for z: $7(8)+6z=26$
$6z=-30$
$z=-5$
Solve for x: $-x+2(8)+(-5)=11$
$-x=0$
$x=0$
