#### Answer

$x=4$
$ y=-3$
$z=2 $

#### Work Step by Step

Write the augmented matrix of the system of linear equations.
$ \begin{bmatrix}
1 &0 & -3 & -2\\
3 & 1 & -2 & 5\\
2 & 2 &1 & 4
\end{bmatrix} $
Add -3 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 &0 & -3 & -2\\
0 & 1 & 7 & 11\\
0 & 2 &7 &8
\end{bmatrix} $
Add -2 times the 2nd row to the 3rd row to produce a new 3rd row.
$ \begin{bmatrix}
1 &0 & -3 & -2\\
0 & 1 & 7 & 11\\
0 & 0 &-7 & -14
\end{bmatrix} $
Divide the third row by -7.
$ \begin{bmatrix}
1 &0 & -3 & -2\\
0 & 1 & 7 & 11\\
0 & 0 &1 & 2
\end{bmatrix} $
Use back-substitution to find the solution.
$z=2 $
$y+7z=11 \rightarrow y=-3$
$x-3z=-2 \rightarrow x=4$