Question

Solve the equation $\frac{x}{a}+\frac{y}{b}=2,ax-by=a^2-b^2$

Answer 1

Consider the given equation.

$ax-by=a^2-b^2$

Multiplying by $a$ in both sides,

$a^{2}x-yab=a^3-a{b}^2$ ......(1)

Since,

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

$xb+ya=2ab$

Multiplying by $b$ in both sides,

$x{b}^2+yab=2a{b}^2$ ......(2)

On adding equation(1) and (2),

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

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

$x=a$

Substituting this value in equation (1),

$a\times a^2-yab=a^3-a{b}^2$

$-yab=a{b}^2$

$y=b.$

So, for given equation $x=a,y=b.$