Question

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

Answer 1

Given,

$bx+ay=2ab$...(1)

$ax+by=a^2+b^2$...(2)

$\left(1\right)÷b-\left(2\right)÷a=$

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

$\left(\frac{a^2-b^2}{ab}\right)y=\frac{2a^2-a^2-b^2}{a}$

$(a^2-b^2)y=b(a^2-b^2)$

$\Rightarrow y=b$

From (1)

$bx+ay=2ab$

$bx+ab=2ab$

$bx=ab$

$\Rightarrow x=a$