Answer
Solution set = $\displaystyle \{(\frac{1}{3},\frac{2}{3})\}$
Work Step by Step
Reduce the augmented matrix $[A|B]$ to reduced row echelon form and interpret the result
$\left[\begin{array}{lll}
3 & 3 & 3\\
4 & 2 & 8/3
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}\div 3.\\
R_{2}=3r_{2}-4r_{1}
\end{array}\right)$
$\rightarrow\left[\begin{array}{lll}
1 & 1 & 1\\
0 & -6 & -4
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
R_{2}=-\frac{1}{6}r_{2}
\end{array}\right)$
$\rightarrow\left[\begin{array}{lll}
1 & 1 & 1\\
0 & 1 & 2/3
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}-r_{2}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{lll}
1 & 0 & 1/3\\
0 & 1 & 2/3
\end{array}\right]$
The system is consistent and has a single solution.
$x=1/3,$
$y=2/3$
Solution set = $\displaystyle \{(\frac{1}{3},\frac{2}{3})\}$