Answer
$x_1=1, \quad x_2=4 , \quad x_3=-3, \quad x_4=-2.$$
Work Step by Step
The augmented matrix is given by
$$
\left[ \begin {array}{ccccc} 2&1&1&2&-1\\ 5&-2&1&-3
&0\\ -1&3&2&2&1\\ 3&2&3&-5&12
\end {array} \right]
.
$$
Using Gauss-Jordan elimination, we get the row-reduced echelon form as follows
$$\left[ \begin {array}{ccccc} 1&0&0&0&1\\ 0&1&0&0&4
\\ 0&0&1&0&-3\\ 0&0&0&1&-2
\end {array} \right]
.$$
From which we get the solution
$$x_1=1, \quad x_2=4 , \quad x_3=-3, \quad x_4=-2.$$
