Answer
The solution set is $\{(2,3)\}$.
Work Step by Step
Multiply the second equation by $-4$ to obtain the equivalent system:
\begin{align*}12x-5y&=9 \quad \quad\quad&(1)\\ -12x+32y&=72 \quad \quad&(2)\end{align*}
Add equations $(1)$ and $(2)$ to eliminate $x$ and then solve for $y$.
\begin{align*}
12x-5y+(-12x+32y)&=9+72 \\ 27y&=81 \\ y&=3
\end{align*}
Plug $y=3$ into the first equation then solve for $x$ to obtain:
\begin{align*}
12x-(5)(3)&=9 \\ 12x-15&=9 \\x&=2
\end{align*}
Thus, the solution set is $\{(2,3)\}$.