Answer
Solution set = $\displaystyle \{( \frac{4}{3} ,\ \frac{1}{5} )\}$
Work Step by Step
Reduce the augmented matrix $[A|B]$ to reduced row echelon form and interpret the result
$\left[\begin{array}{llll}
3 & -5 & | & 3\\
15 & 5 & | & 21
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
R_{2}=r_{2}-5r_{1}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
3 & -5 & | & 3\\
0 & 30 & | & 6
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=r_{1}+\frac{1}{6}r_{2}.\\
R_{2}=\frac{1}{30}r_{2}
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
3 & 0 & | & 4\\
0 & 1 & | & 1/5
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}=\frac{1}{3}r_{1}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 0 & | & 4/3\\
0 & 1 & | & 1/5
\end{array}\right]$
The system is consistent and has a single solution.
$x=4/3,$
$y=1/5$
Solution set = $\displaystyle \{( \frac{4}{3} ,\ \frac{1}{5} )\}$
