Question

Solve for $x$ and $y$ :
$\frac{bx}{a}+\frac{ay}{b}=a^2+b^2$
$x+y=2ab$

Answer 1

$\frac{bx}{a}+\frac{ay}{b}=a^2+b^2$

$\Rightarrow b^{2}x+a^{2}y=a^{3}b+b^{3}a.....\left(1\right)$

$x+y=2ab.....\left(2\right)$

Multiplying equation $\left(2\right)$ by $b^2$, we get

$a^{2}x+a^{2}y=2a^{3}b.....\left(3\right)$

Subtracting equation $\left(3\right)$ from $\left(1\right)$, we have

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

$\Rightarrow x=\frac{ab(b^2-a^2)}{(b^2-a^2)}=ab$

Putting $x=ab$ in equation $\left(2\right)$, we have

$ab+y=2ab$

$\Rightarrow y=2ab-ab=ab$

Hence $x=ab=y$