Answer
Solution set = $\{( 2 ,\ -3 )\}$
Work Step by Step
Reduce the augmented matrix $[A|B]$ to reduced row echelon form and interpret the result
$\left[\begin{array}{llll}
1/2 & 1 & | & -2\\
1 & -2 & | & 8
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=2r_{1}.\\
R_{2}=r_{2}-2r_{1}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 2 & | & -4\\
0 & -4 & | & 12
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
R_{2}=-\frac{1}{4}r_{2}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 2 & | & -4\\
0 & 1 & | & -3
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}-2r_{2}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 0 & | & 2\\
0 & 1 & | & -3
\end{array}\right]$
The system is consistent and has a single solution.
$x=2,$
$y=-3$
Solution set = $\{( 2 ,\ -3 )\}$
