Answer
$(0,-2,6)$ is a solution of the system.
Work Step by Step
Use elimination for the first and the third equation:
$-x + 5y- z=-16$
$x + y -z =-8$
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$6y-2z=-24$ (1)
Then continue to use elimination for the first and second equation:
$x + y -z =-8$
$2x + 3y +4z= 18$
Multiply both sides of the first equation by $-2$
$-2x -2y +2z =16$
$2x + 3y +4z= 18$
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$y+6z=34$ (2)
From (1) and (2):
$6y-2z=-24$
$y+6z=34$
Multiply both sides of the first equation by $3$:
$18y-6z=-72$
$y+6z=34$
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$19y=-38$
$y=-2$
Solve for z: $-2+6z=34$
$z=6$
Solve for x: $x+(-2)-6=-8$
$x=0$
$(0,-2,6)$ is a solution of the system.
