Answer
$$x_1=\frac{6}{7}, \quad x_2=-{\frac {
23}{7}}.$$
Work Step by Step
The system can written on the form $Ax=b$ as follows
$$x_1\left[ \begin {array}{c} {2} \\{3} \end {array} \right]+x_2\left[ \begin {array}{c} {-1}\\ {2} \end {array} \right]=\left[ \begin {array}{c} {5}\\ {-4} \end {array} \right].$$
To solve system using Gaussian elimination, we form the augmented matrix as follows
$$\left[ \begin {array}{ccc} 2&-1&5\\ 3&2&-4
\end {array} \right]
.
$$
The reduced row echelon form is given by
$$\left[ \begin {array}{ccc} 1&0&\frac{6}{7}\\ 0&1&-{\frac {
23}{7}}\end {array} \right]
.
$$
From which, we have
$$x_1=\frac{6}{7}, \quad x_2=-{\frac {
23}{7}}.$$
