Answer
Solution set = $\{( 0.5 ,\ 2 )\}$
Work Step by Step
Reduce the augmented matrix $[A|B]$ to reduced row echelon form and interpret the result
$\left[\begin{array}{llll}
2 & -1 & | & -1\\
1 & 0.5 & | & 1.5
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
R_{2}=2r_{2}-r_{1}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
2 & -1 & | & -1\\
0 & 2 & | & 4
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
R_{2}=0.5r_{2}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
2 & -1 & | & -1\\
0 & 1 & | & 2
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}+r_{2}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
2 & 0 & | & 1\\
0 & 1 & | & 2
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=0.5r_{1}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 0 & | & 0.5\\
0 & 1 & | & 2
\end{array}\right]$
The system is consistent and has a single solution.
$x=0.5,$
$y=2$
Solution set = $\{( 0.5 ,\ 2 )\}$