Solve for 'x' and 'y': `(a -b) x + (a + b) y =a^2 - b^2 - 2ab (a + b) (x + y) = a ^2+ b^2`

Explanation

Given equations are (a - b) x + (a + b) `y = a^(2) - 2ab - b^(2) ….(1)`
and (a + b) (x + y) = `a^(2) + b^(2)`
or (a + b)x + (a + b) `y = a^(2) + b^(2) …..(2)`
On subtracting equation (2) from (1), we get
`(a-b)x - (a + b) x = a^(2) - 2ab - b^(2) -a^(2) -b^(2)`
implies x(a-b-a-b) = - `2b^(2) - 2ab`
implies -2bx = - 2b (b + a)
implies x = a + b
Putting x = (a + b) in equation (1), we get
`(a-b)(a+b)+(a+b) y = a^(2) - 2ab -b^(2)`
implies `a^(2) - b^(2) + (a + b) y = a^(2) - 2ab - b^(2)`
implies `(a + b) y = - 2ab`
` implies y = (-2ab)/(a+b)`
Hence, the solution is `{:(x = a + b),(y = (-2ab)/(a+b)):}}`.