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 - b2 ............. (1)
(a+b)(x+y) = a2 + b2 ............ (2)
Considering equation (2),
(a+b)(x+y) = a2+ b2
(a+b)x + (a+b)y =a2+ b2 ............ (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... :)