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... :)

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