Answer
The solution set is $\left\{ \left( -5,-1 \right) \right\}$.
Work Step by Step
By rewriting the system as:
$\begin{align}
& x-y=-4 \\
& x+4y=-9
\end{align}$
We subtract the second equation from the first equation to obtain:
$\begin{align}
& x-y-x-4y=-4-\left( -9 \right) \\
& -5y=-4+9 \\
& -5y=5 \\
& y=-1
\end{align}$
Substitute the value of y in the first equation and solve for x:
$\begin{align}
& x-\left( -1 \right)=-4 \\
& x+1=-4 \\
& x=-4-1 \\
& =-5
\end{align}$.
Thus, The solution set is $\left\{ \left( -5,-1 \right) \right\}$.
