Answer
$x=-5,\ y=7$
or $(-5,7)$
Work Step by Step
Method: Gauss-Jordan. Row reduce the augmented matrix:
$\left[\begin{array}{rr|r}
2 & 3 & 11 \\
5 & 7 & 24 \end{array}\right]\qquad\left\{\begin{array}{l}
R_{1}=3r_{1}-r_{2}\\
.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 2 & 9 \\
5 & 7 & 24 \end{array}\right]\qquad\left\{\begin{array}{l}
.\\
R_{2}=r_{2}-5r_{1}.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 2 & 9 \\
0 & -3 & -21 \end{array}\right]\qquad\left\{\begin{array}{l}
.\\
R_{2}=-r_{2}\div 3.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 2 & 9 \\
0 & 1 & 7 \end{array}\right]\qquad\left\{\begin{array}{l}
R_{1}=r_{1}-2r_{2}.\\
.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 0 & -5 \\
0 & 1 & 7 \end{array}\right]$
Solution: $x=-5,\ y=7$ or $(-5,7)$
