Question

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

Answer 1

$\frac{x}{a}+\frac{y}{b}=2$

multiply by $ab$ both side, we get

$\Rightarrow bx+ay=2ab\dots \dots \left(1\right)$

$ax-by=a^2-b^2\dots \dots \left(2\right)$

multiply (1) by a and (2) by b

From $\left(1\right)\times a-\left(2\right)\times b$, we get

$y(a^2+b^2)=2a^{2}b-a^{2}b+b^3$

$\Rightarrow y(a^2+b^2)=a^{2}b+b^3=b(a^2+b^2)$

$\Rightarrow y=b\dots \dots \left(3\right)$

Put eqn (3) in eqn (1), we get

$\Rightarrow bx+ab=2ab\Rightarrow x=a$

therefore values for $x$ and $y$ are $a$ and $b$ respectively.