Answer
$\{(2,3)\}$
Work Step by Step
Start with the augmented matrix and attempt to reduce it to diagonal form, with 1s along the diagonal.
$\left[\begin{array}{llll}
1 & 1 & | & 5\\
1 & -1 & | & -1
\end{array}\right]\left\{\begin{array}{l}
.\\
\leftarrow(R_{2}-R_{1}).
\end{array}\right.$
$\left[\begin{array}{llll}
1 & 1 & | & 5\\
0 & -2 & | & -6
\end{array}\right]\left\{\begin{array}{l}
.\\
\leftarrow(-R_{2}/2).
\end{array}\right.$
$\left[\begin{array}{llll}
1 & 1 & | & 5\\
0 & 1 & | & 3
\end{array}\right]\left\{\begin{array}{l}
\leftarrow(R_{1}-R_{2}).\\
.
\end{array}\right.$
$\left[\begin{array}{llll}
1 & 0 & | & 2\\
0 & 1 & | & 3
\end{array}\right]$
$x=2$
$y=3$
Solution set: $\{(2,3)\}$
