`(ax)/b-(by)/a=a+b`, `ax-by=2ab`

Explanation

The given equation may be written as
` a ^(2) x - b ^(2) y = a ^(2) b + ab ^(2)" "`...(i)
` ax - by = 2ab" " `...(ii)
Multiplying (ii) by b and subtracting the result from (i) we get
` (a ^(2) - abx ) x = a ^(2) b - ab ^(2) `
`rArr (a ^(2) - ab) x = b ( a ^(2) - ab ) rArr x = b `.
Putting ` x = b ` in (ii), we get
` ab - by = 2ab rArr by = - ab rArr y = (-ab)/(b) = - a `
Hence, ` x = b and y = - a `