Solve the following system of equations
bx + ay = 2ab and `ax - by = a^(2) - b^(2)`.

Explanation

Given equations can be written as
bx + ay - 2ab = 0
and ax - by - `a^(2) + b^(2) = 0`
By cross multiplication method, we have

`(x)/(axx [-(a^(2) - b^(2))]-(-b)xx(-2ab))=(y)/((-2ab) xx a - [-(a^(2)-b^(2))]xxb)=(1)/(b xx (-b)- a xx a)`
`implies (x)/(a(-a^(2)+b^(2)-2ab^(2)))=(y)/(-2a^(2)b+a^(2)b-b^(3))=(1)/(-b^(2)-a^(2))`
implies `(x)/(a(-a^(2)-b^(2)))=(y)/(-a^(2)b-b^(3))=(1)/(-b^(2)-a^(2))`
when `(x)/(a(-a^(2)-b^(2)))=(1)/(-b^(2)-a^(2))`
`implies x = (-a(a^(2) + b^(2)))/(-1(b^(2) + a^(2))) or x = a `
and `(y)/(-a^(2)b-b^(3))=(1)/(-b^(2)-a^(2))`
implies `y = (-b(a^(2) + b^(2)))/(-1(b^(2) + a^(2))) or y = b`
Hence, `{:(x=a),(y=b):}}` is the required solution.