Answer
$x=-2, y=1 \text{ or } (-2,1)$
Work Step by Step
We will write the system $\left\{\begin{array}{r}{2x+y=-3}\\{ax+ay=-a}\end{array}\right.$ in matrix form as: $AX=B$
where, $X=\left[\begin{array}{l}x\\y \end{array}\right]$
We have: $A=\left[\begin{array}{ll}{2}&{1}\\{a}&{a}\end{array}\right]$, and its inverse is: $A^{-1}=\left[\begin{array}{rr}{1}&{-1/a}\\{-1}&{2/a}\end{array}\right]$
Thus, the solution of the given matrix can be expressed as:
$X=A^{-1}B=\left[\begin{array}{rr}{1}&{-1/a}\\{-1}&{2/a}\end{array}\right]\left[\begin{array}{l}
-3\\-a\end{array}\right]$
$\left[\begin{array}{l}
x\\y \end{array}\right]=\left[\begin{array}{l} -3+1\\
3-2 \end{array}\right]=\left[\begin{array}{l}
-2\\1\end{array}\right]$
So, our solution is:: $(x, y)=(-2,1)$
