- by = a^2 + b^2 [Equation 1]

x + y= 2a [Equation 2]

Multiply Equation 2 by b

=> bx + by= 2 ab [Equation 3]

Add Equation 1 and 3

⇒ ax + bx - by + by = a^2 + b^2 + 2ab

⇒ (a + b)x = a^2 + b^2 + 2ab = (a + b)^2 [Using Identity we get]

$$\bf\huge{\implies x = \dfrac{(a+b)^2}{a+b} = a + b}$$

Put value x in Equation (2)

(a + b) + y = 2a

y = 2a - (a + b)

y = 2a - a - b

y = a - b