Answer
The solution set is $\{(2,-2)\}$
Work Step by Step
Write each equation in standard form to obtain:
\begin{align*} 6x+7y=-2 ~~~&(1) \\ 7x-6y=26 ~~~&(2)\end{align*}
Multiply the first equation by $6$ and second equation by $7$ to obtain the equivalent system:
\begin{align*}36x+42y=-12 ~~~&(3) \\ 49x-42y=182 ~~~&(4)\end{align*}
Add equations $(3)$ and $(4)$ to eliminate $y$ and then solve for $x$.
\begin{align*}36x+42y+49x-42y&=-12+182 \\ 85x&=170 \\ x&=2\end{align*}
Plug $x=2$ into the first equation then solve for $y$ to obtain:
\begin{align*}(6)(2)+7y&=-2 \\ 12+7y&=-2\\ y&=-2\end{align*}
Thus, the solution set is $\{(2,-2)\}$