Answer
$x=-1$
$y=5$
$z=0$
Work Step by Step
$ \begin{bmatrix}
1 & 2 & -1 & 9\\
2 & 0 & -1 & -2\\
3 & 5 & 2 & 22
\end{bmatrix} $
Add -2 times the 1st row to the 2nd row to produce a new 2nd row.
Add -3 times the 1st row to the 3rd row to produce a new 3rd row.
$ \begin{bmatrix}
1 & 2 & -1 & 9\\
0 & -4 & 1 & -20\\
0 & -1 & 5& -5
\end{bmatrix} $
Interchange the 2nd and the 3rd row.
$ \begin{bmatrix}
1 & 2 & -1 & 9\\
0 & -1 & 5& -5\\
0 & -4 & 1 & -20
\end{bmatrix} $
Divide the second row by -1.
$ \begin{bmatrix}
1 & 2 & -1 & 9\\
0 & 1 & -5& 5\\
0 & -4 & 1 & -20
\end{bmatrix} $
Add 4 times the 2nd row to the 3rd row.
$ \begin{bmatrix}
1 & 2 & -1 & 9\\
0 & 1 & -5& 5\\
0 & 0 & -19 & 0
\end{bmatrix} $
Use back-substitution to find the solution.
$-19z=0 \rightarrow z=0$
$y-5z=5\rightarrow y=5$
$x+2y-y=9 \rightarrow x=-1$
