## Precalculus (6th Edition) Blitzer

The solution of the system of equations is $\left( x,y \right)=\left( \frac{1}{a},3 \right)$.
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}