Question

Solve for x and y
$\frac{ax}{b}-\frac{by}{a}=a+b$, $ax-by=2ab$

Answer 1

equation (1) $\times b\Rightarrow ax-\frac{b^{2}y}{a}=ab+b^2$

and $\frac{ax-by=2ab}{(b-\frac{b^2}{a})y=-ab+b^2}$

$\Rightarrow (ab-b^2)y=-a(ab-b^2)\Rightarrow y=-a$

By equation (2), $ax+ab=2ab\Rightarrow ax=ab\Rightarrow x=b$