slove for x and y

(a-b)x + (a+b)y = a² - 2ab - b² .......(1)

(a+b)(x-y) = a² + b²   ............(2)

Adding (1) and (2),

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

2ax = 2a² - 2ab

x = (a - b)

Use this result in (2) to find y,

(a+b)(x-y) = a² + b² 

(x-y) = (a² + b²)/(a+b)

y = (a - b) - (a² + b²)/(a+b)

= [(a - b)(a+b) - (a² + b²)]/(a+b)

= -2b²/(a+b)

Regards,

Team,

TopperLearning.