Answer
$x=-1,$
$y=-2,$
$z=4$
Work Step by Step
$\begin{cases}
2x+y-z=-8\\
-x+y+z=3\\
-2x+4z=18
\end{cases}$
Adding Equation 1 and Equation 3, results in new Equation 1.
$\begin{cases}
2x+y-z=-8\\
-2x+4z=18\\
-- -- -- --\\
y+3z=10
\end{cases}$
Multiplying Equation 2 by -2 and adding it to Equation 3, results in new Equation 2.
$\begin{cases}
2x-2y-2z=-6\\
-2x+4z=18\\
-- -- -- --\\
-2y+2z=12
\end{cases}$
Multiplying new Equation 1 by 2 and adding it to new Equation 2.
$\begin{cases}
-2y+2z=12\\
2y+6z=20\\
-- -- --\\
8z=32
\end{cases}$
Thus, $z=4$. Substituting it back into new Equation 1, $y+12=10, y=-2$. Substituting it back into Equation 2, $-x-2+4=3, x=-1$
