Answer
$x=-1,$
$y=1,$
$z=2$
Work Step by Step
$\begin{cases}
x-y+2z=2\\
3x+y+5z=8\\
2x-y-2z=-7
\end{cases}$
Multiplying Equation 1 by -2 and adding it to Equation 3, results in new Equation 3.
$\begin{cases}
-2x+2y-4z=-4\\
2x-y-2z=-7\\
-- -- -- -- --\\
y-6z=-11
\end{cases}$
Multiplying Equation 1 by -3 and adding it to Equation 2, results in new Equation 2.
$\begin{cases}
-3x+3y-6z=-6\\
3x+y+5z=8\\
-- -- -- -- --\\
4y-z=2
\end{cases}$
Multiplying new Equation 3 by -4 and adding it to new Equation 2.
$\begin{cases}
-4y+24z=44\\
4y-z=2\\
-- -- --\\
23z=46
\end{cases}$
Thus, $z=2$. Susbtituting it back into new Equation 3, $y-12=-11, y=1$. Substituting it back into Equation 1, $x-1+4=2, x=-1$
