Answer
$x=1,$
$y=0,$
$z=-1$
Work Step by Step
$\begin{cases}
x-y+z=0\\
0x+y+2z=-2\\
x+y-z=2
\end{cases}$
Adding Equation 1 and Equation 3.
$\begin{cases}
x-y+z=0\\
x+y-z=2\\
-- -- -- --\\
2x=2
\end{cases}$
Thus, $x=1$. Substituting back into Equation 1 becomes
$-y+z=-1$.
Adding Equation 1 and Equation 2.
$\begin{cases}
-y+z=-1\\
y+2z=-2\\
-- -- --\\
3z=-3
\end{cases}$
Thus, $z=-1$. Substituting back into the Equation 1, $1-y-1=0, y=0$
