Answer
The solution set is $\{(1, 3)\}$.
Work Step by Step
We are given the system of equations as:
$2x-3y=-7 ~~~(1) \\ -5x-4y=-17 ~~~(2)$
By multiplying equation $(1)$ by $5$ and equation $(2)$ by $2$, then first and second equation are equivalent to:
$10x-15y=-35 ~~~(3) \\
-10x-8y=-34 ~~~(4)$
Add equations $(3)$ and $(4)$ to eliminate $x$ and then solve for $y$.
\begin{align*}
10x-15y+(-10x-8y)&=-35 +(-34) \\ 10x-15y-10x-8y&=-69 \\ -23 y&=-69 \\ y&=3
\end{align*}
Plug $y=3$ into the first equation then solve for $x$ to obtain:
\begin{align*}
2x-(3)(3)=-7 \\ 2x-9=-7 \\x=1
\end{align*}
So, the solution set is $\{(1, 3)\}$.