Answer
The solution set is $\left\{(0, 4)\right\}$.
Work Step by Step
To eliminate $y$, we multiply $3$ to both sides of the first euation to obtain:
$$3(3x-y)=3(-4) \implies 9x-3y=-12$$
The system of equations becomes
\begin{align*}
9x-3y&=-12\\
x+3y&=12\end{align*}
Now, we can add the two equations together to eliminate $y$, to obtain:
\begin{align*}
&9x-3y=-12\\
&\underline{\space \space x+3y=12}\\
&10x \space \space \space \space \space \space =0
\end{align*}
Dividing both sides by $10$ gives $x=0$.
Substitute $0$ to $x$ in the first equation to obtain:
$3(0)-y=-4 \\ \implies -y=-4\\
\implies y=4$