Question

solve for x and y b/a x + a/b y = a^2- b ^2 :, x +y =2ab

Answer 1

(b/a) x + (a/b) y = a² - b²
taking LCM b² x + a² y = (a² - b²) ab --------(1)
also given x + y = 2 ab ------(2)
multiplying (2) by b² we get
x b² + y b² = 2 ab³ -------(3)
solving (1) and (3), we get 
 y = (a² - b²) ab/(a² - b²) - 2 ab³/(a²-b²)
y = ab - 2 ab³/(a²-b²)

substituting y value in (2) 

x + ab - 2 ab³/ (a²-b²) = 2 ab
x = 2 ab - ab + 2 ab³/ (a²-b²)
x = ab + 2 ab³ /( a²-b²)
verification: substitute the x and y values in (2) we get 2 ab