Question

Solve for $x$ and $y$ : $\frac{x}{a}-\frac{y}{b}=a-b$, $ax+by=a^3+b^3$.

Answer 1

$x=(\frac{y}{b}+a-b)\times a$

$ax+by=by+a^2\frac{y}{b}+a^3-a^{2}b=a^3+b^3$

$\Rightarrow y\left(\frac{b^2+a^2}{b}\right)=64+a^2{b}^2$

$\Rightarrow y=\frac{(b^2+a^2)b^2}{(a^2+b^2)}=b^2$

$x=(b+a-b)a=a^2$

$\Rightarrow x=a^2,y=b^2$