Answer
$x=-1$
$y=-2$
$z=4$
Work Step by Step
Express x from the second equation.
$2x+y-z=-8 $
$-x+y+z=3 \rightarrow x=y+z-3$
$-2x+4z=18$
Substitute $ x=y+z-3$ into the first and the third equation.
$2(y+z-3)+y-z=-8 $
$-2(y+z-3)+4z=18$
Simplify.
$3y+z=-2$
$-2y+2z=12$
Multiply the first equation by -2.
$3y+z=-2 \rightarrow -6y-2z=4$
Add the equations to eliminate z.
$-8y=16$
$y=-2$
Substitute for y and solve for x and z.
$3y+z=-2 \rightarrow z=4$
$x=y+z-3 \rightarrow x=-1$
