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