Question

Solve for x and y ax/b-by/a=a+b, ax - by =2ab

Answer 1

not able to solve x-y.

Answer 2

Answer:

We solve the given system of equation by substitution method.

$\frac{ax}{b}-\frac{by}{a}=a+b$ ...................... (1)

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

First we find value of x from (2)

from (2), we get

$ax=2ab+by$

$x=\frac{2ab+by}{a}$ ......... (3)

Now, We put value of x from (3) in (1), to get the value of y.

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

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

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

$2a^2b-aby+b^2y=ab(a+b)$

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

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

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

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

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

$y=-a$

Finally to find the value of x we put value of y in (3)

$x=\frac{2ab-ba}{a}$

$x=\frac{ab}{a}$

$x=b$

Therefore, We get Value x = b & y = -a