Question

Solve

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

$ax-by=2ab$

Answer 1

We have,

$\frac{a}{b}x-\frac{b}{a}y=a+b$ ........(1)

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

Dividing equation (2) by 'a' on both sides

$x-\frac{b}{a}y=2b$ .............(3)

Subtracting equation (3) from equation (1), we get

$(\frac{a}{b}-1)x=a-b$

$\frac{(a-b)}{b}x=a-b$

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

$\Rightarrow x=b$

Now,

Dividing equation 2 by 'b' on both, we get

$\frac{a}{b}x-y=2a$ .........(4)

Subtraction equation 4 from equation 1, we get

$(1-\frac{b}{a})y=b-a$

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

$\Rightarrow y=\frac{a(b-a)}{(a-b)}$

$\Rightarrow y=-a$

$\therefore x=bandy=-a$