Answer
Solution set = $\displaystyle \{(\frac{1}{2},\frac{3}{4})\}$
Work Step by Step
Reduce the augmented matrix $[A|B]$ to reduced row echelon form and interpret the result
$\left[\begin{array}{lll}
2 & -4 & -2\\
3 & 2 & 3
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{2}-r_{1}.\\
R_{2}=3r_{2}-2r_{1}
\end{array}\right)$
$\rightarrow\left[\begin{array}{lll}
1 & 6 & 5\\
0 & -16 & -12
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
R_{2}=-\frac{1}{16}r_{2}
\end{array}\right)$
$\rightarrow\left[\begin{array}{lll}
1 & 6 & 5\\
0 & 1 & 3/4
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}-6r_{2}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{lll}
1 & 0 & 1/2\\
0 & 1 & 3/4
\end{array}\right]$
The system is consistent and has a single solution.
$x=1/2,$
$y=3/4$
Solution set = $\displaystyle \{(\frac{1}{2},\frac{3}{4})\}$
