Answer
$x=1$
$y=-1$
$z=5$
Work Step by Step
Express y from the second equation.
$x+2y-z=-6$
$y-3z=-16\rightarrow y=-16+3z$
$x-3y+2z=14$
Substitute $ y=-16+3z$ into the first and the third equation.
$x+2(-16+3z)-z=-6$
$x-3(-16+3z)+2z=14$
Simplify.
$x+5z=26$
$x-7z=-34$
Multiply the second equation by -1.
$x-7z=-34 \rightarrow -x+7y=34$
Add the equations to eliminate x.
$12z=60$
$z=5$
Substitute for z and solve for x and y.
$x+5z=26 \rightarrow x=1$
$y=-16+3z \rightarrow y=-1$