Answer
$(x,y)=(2/a,3/a)$
Work Step by Step
This problem is connected to exercise $35$, as the coefficient matrix of the system
$\displaystyle \left\{\begin{aligned}2x+y&=\displaystyle \frac{7}{a}\\ax+ay&=5\displaystyle \end{aligned}\right.$
is
$\left[\begin{array}{ll}{2}&{1}\\{a}&{a}\end{array}\right]\quad a\neq 0$
and we found
$A^{-1}=\left[\begin{array}{rr}
{1}&{-1/a}\\
{-1}& {2/a}\end{array}\right]$
Writing the system in matrix form, $AX=B,$ the solution is
$X=A^{-1}B$
$\left[\begin{array}{l}
x\\
y
\end{array}\right]=\left[\begin{array}{rr}
{1}&{-1/a}\\
{-1}& {2/a}\end{array}\right] \left[\begin{array}{l}
7/a\\
5
\end{array}\right]$
$\left[\begin{array}{l}
x\\
y
\end{array}\right]=\left[\begin{array}{l}
\frac{7}{a}-\frac{5}{a}\\
-\frac{7}{a}+\frac{10}{a}
\end{array}\right]=\left[\begin{array}{l}
2/a\\
3/a
\end{array}\right]$
Solution: $(x,y)=(2/a,3/a)$
