Question

Solve for $x$ and $y.$

$\begin{array}{c}\frac{x}{b}+\frac{y}{a}=2,ax-by=a^2-b^2\end{array}$

Answer 1

$\frac{x}{b}+\frac{y}{a}=2,ax-by=a^2-b^2$

$ax+by=2ab,ax-by=a^2-b^2$

add both

$2ax=2ab+a^2-b^2$

$x=b+\frac{a^2-b^2}{2a}$

subtract the both

$2by=2ab+b^2-a^2$

$y=a+\frac{b^2-a^2}{2b}$