Answer
The solution of the system of equations is $\left( x,y \right)=\left( \frac{1}{a},3 \right)$.
Work Step by Step
Let us consider the equations (I) and (II) as follows:
$\begin{align}
& 5ax+4y=17 \\
& ax+7y=22
\end{align}$
And multiply equation (I) by 7 to obtain equation (III):
$35ax+28y=119$
Then, multiply equation (II) by to obtain equation (IV):
$-4ax-28y=-88$
And add equations (III) and (IV):
$\begin{align}
& 35ax+28y-4ax-28y=119-88 \\
& 31ax=31 \\
& x=\frac{1}{a}
\end{align}$
Substitute the value of x in equation (II)
$\begin{align}
& 1+7y=22 \\
& 7y=21 \\
& y=3
\end{align}$
