Answer
$(2,2,-1)$ is the solution of the system.
Work Step by Step
Using elimination for the second and the third equations:
$x -3y +2z = -6$
$-x + 2y - z = 3$
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$-y+z=-3$ (1)
Then continue to use elimination for the second and the third equations:
$4x + 5y + 3z = 15 $
$x -3y +2z = -6$
Multiply both sides of the second equation by $-4$:
$4x + 5y + 3z = 15 $
$-4x + 12y - 8z = 24$
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$17y-5z=39$
Using elimination for equations (1) and (2):
$-y+z=-3$
$17y-5z=39$
Multiply both sides of the first equation by $5$:
$-5y+5z=-15$
$17y-5z=39$
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$12y=24$
$y=2$
Solve for z: $-y+z=-3$
$-2+z=-3$
$z=-1$
Solve for x: $x-3y+2z=-6$
$x-3(2)+2(-1)=-6$
$x=2$
$(2,2,-1)$ is the solution of the system.
