Answer
$x=3$
$y=-1$
$z=-4$
Work Step by Step
Using elimination for the first two equations:
$2x+y-z=9$
$-x+6y+2z=-17$
Multiply both sides of the first equation by $2$
$4x+2y-2z=18$
$-x+6y+2z=-17$
_________________________
$3x+8y=1$ (1)
Using elimination for the first and the third equations:
$2x+y-z=9$
$5x+7y+z=4$
_________________________
$7x+8y=13$ (2)
From (1) and (2):
$3x+8y=1$
$7x+8y=13$
Multiply both sides of the first equation by $-1$
$-3x-8y=-1$
$7x+8y=13$
___________________
$4x=12$
$x=3$
Solve for y: $3(3)+8y=1$
$9+8y=1$
$8y=-8$
$y=-1$
Solve for z: $2(3)+(-1)-z=9$
$-z=4$
$z=-4$
