Solve (a-b)x + (a+b)y = asquare - 2ab - b square and (a+b)(x+y) = a square +b square.

(a-b)x + (a+b)y =a² - 2ab - b^{2 ............. (1)}

(a+b)(x+y) = a² + b^{2 ............ (2)}

Considering equation (2),

(a+b)(x+y) = a²+ b²

(a+b)x + (a+b)y =a²+ b^{2 ............ (3)}

Further, you can subtract equation (3) from equation (1) by elimination method because the coeffecients of y terms are same in both the equations.

The difference thus obtained will be,

(a-b)x - (a+b)x = a²- 2ab - b²- (a²+ b²)

ax - bx - ax - bx = a²- 2ab - b²- a²- b²

-2bx = -2ab -2b²

x = -2ab -2b²/ -2b

x = -2b (a+b) / -2b (Taking -2b common in the numerator and denominator and cancelling)

therefore, x = a+b

Substitutingx = a+b in equation (1),

(a-b)x + (a+b)y =a²- 2ab - b²

(a-b) (a+b) + (a+b)y =a²- 2ab - b²

(a²- b²) + (a+b)y = a²- 2ab - b²

(a+b)y =a²- 2ab - b²-(a²- b²)

(a+b)y = a²- 2ab - b²- a² +b²

(a+b)y = -2ab

y = -2ab / a+b

Therefore,

x = a+b , y = -2ab / a+b

Hope it Helps... :)