Answer
$x=2,$
$y=3,$
$z=-2$
Work Step by Step
$\begin{cases}
x-2y+3z=-10\\
0x+3y+z=7\\
x+y-z=7
\end{cases}$
Multiplying Equation 3 by -1 and adding it to Equation 1, results in new Equation 3.
$\begin{cases}
x-2y+3z=-10\\
-x-y+z=-7\\
-- -- -- -- \\
-3y+4z=-17
\end{cases}$
Adding new Equation 3 and Equation 2.
$\begin{cases}
-3y+4z=-17\\
3y+z=7\\
-- -- -- --\\
5z=-10
\end{cases}$
Thus, $z=-2$. Substituting back into Equation 2, $3y-2=7, y=3$.
Substituting back into Equation 1, $x-6-6=-10, x=2$.
