Question

Solve:

$\frac{ax}{b}-\frac{by}{a}=a+b$
$ax-by=2ab$.

Answer 1

First equation is,

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

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

$a^{2}x-b^{2}y=a^{2}b+a{b}^2$ ........... (1)

second equation is,

$ax-by=2ab$ ...............(2)

Multiply the above equation by $a$

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

Subtract (3) from (1),

$-b^{2}y+aby=a^{2}b+a{b}^2-2a^{2}b$

$-b^{2}y+aby=-a^{2}b+a{b}^2$

$b(-b+a)y=-ab(a-b)$

$by=-ab$

$y=-a$

From equation (1),

$ax-by=2ab$

$ax-b(-a)=2ab$

$ax=2ab-ab$

$ax=ab$

$x=b$