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