Answer
$x=1,$
$y=-1,$
$z=5$
Work Step by Step
$\begin{cases}
x+2y-z=-6\\
0x+y-3z=-16\\
x-3y+2z=14
\end{cases}$
Multiplying Equation 3 by -1 and adding it to Equation 1, results in new Equation 3.
$\begin{cases}
x+2y-z=-6\\
-x+3y-2z=-14\\
-- -- -- -- --\\
5y-3z=-20
\end{cases}$
Multiplying Equation 2 by -5 and adding it to new Equation 3.
$\begin{cases}
-5y+15z=80\\
5y-3z=-20\\
-- -- -- -- \\
12z=60
\end{cases}$
Thus, $z=5$. Substituting back into Equation 2. $y-15=-16, y=-1$.
Substituting back into Equation 1. $x-2-5=-6, x=1$.
