Answer
Solution set = $\{( 1.5 ,\ 1 )\}$
Work Step by Step
Reduce the augmented matrix $[A|B]$ to reduced row echelon form and interpret the result
$\left[\begin{array}{llll}
2 & 3 & | & 6\\
1 & -1 & | & 1/2
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}-r_{2}.\\
R_{2}=2r_{2}-r_{1}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 4 & | & 11/2\\
0 & -5 & | & -5
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
R_{2}=-\frac{1}{5}r_{2}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 4 & | & 11/2\\
0 & 1 & | & 1
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}-4r_{2}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 0 & | & 3/2\\
0 & 1 & | & 1
\end{array}\right]$
The system is consistent and has a single solution.
$x=1.5,$
$y=1$
Solution set = $\{( 1.5 ,\ 1 )\}$