Answer
$(-4,5,-4)$ is the solution of the system.
Work Step by Step
Using elimination for the first two equations:
$2x - y + 2z =-21 $
$x + 5y - z = 25$
Multiply both sides of the second equation by $-2$:
$2x - y + 2z =-21 $
$-2x -10y +2z = -50$
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$-11y+4z=-71$ (1)
Then continue to use elimination for the second and the third equations:
$-3x + 2y + 4z = 6 $
$x + 5y - z = 25$
Multiply both sides of the second equation by $3$:
$-3x + 2y + 4z = 6 $
$3x + 15y - 3z = 75$
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$17y+z=81$ (2)
Using elimination for equations (1) and (2):
$-11y+4z=-71$
$17y+z=81$
Multiply both sides of the second equation by $-4$:
$-11y+4z=-71$
$-68y-4z=-324$
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$-79y=-395$
$y=5$
Solve for z: $17y+z=81$
$17(5)+z=81$
$z=-4$
Solve for x: $2x-y+2z=-21$
$2x-5+2(-4)=-21$
$2x=-8$
$x=-4$
$(-4,5,-4)$ is the solution of the system.
