Answer
$x=8,\ y=-3$
or $(8,-3)$
Work Step by Step
Method: Gauss-Jordan. Row reduce the augmented matrix:
$\left[\begin{array}{rr|r}
2 & 8 & -8 \\
1 & 7 & -13 \end{array}\right]\qquad\left\{\begin{array}{l}
R_{1}=r_{1}-r_{2}\\
.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 1 & 5 \\
1 & 7 & -13 \end{array}\right]\qquad\left\{\begin{array}{l}
.\\
R_{2}=r_{2}-r_{1}
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 1 & 5 \\
0 & 6 & -18 \end{array}\right]\qquad\left\{\begin{array}{l}
.\\
R_{2}=r_{2}\div 6
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 1 & 5 \\
0 & 1 & -3 \end{array}\right]\qquad\left\{\begin{array}{l}
R_{1}=r_{1}-r_{2}\\
.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rr|r}
1 & 0 & 8 \\
0 & 1 & -3 \end{array}\right]$
Solution: $x=8,\ y=-3$
or $(8,-3)$
