Question

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

Answer 1

Given equations are

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

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

$\Rightarrow ay+bx=2ab$ _________ (1)

$ax-by=a^2-b^2$ _______ (2)

From (1) & (2)

Multiply (1) by 'a' (2) by 'b'

$abx+a^{2}y=2a^{2}b$

$abx-b^{2}y=b{a}^2-b^3$

- + -

________________________________

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

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

$\Rightarrow y=b$ [put in equation - 1]

We get

$ay+bx=2ab$

$\Rightarrow a\left(b\right)+bx=2ab$

$\Rightarrow bx=2ab-ab$

$\Rightarrow bx=ab$

$\Rightarrow x=ab/b$

$\Rightarrow x=a$