Solve for x and y:

ax - by = a² + b², x + y = 2a

We have,

ax – by = a² + b² …(i)

x + y = 2a …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply equation (ii) by b, so that variable y in both the equations have same coefficient.

Recalling equations (i) & (ii),

ax – by = a² + b²

x + y = 2a [×b

⇒ ax + bx = a² + b² + 2ab

⇒ (a + b)x = (a + b)²

⇒ x = a + b

Substitute x = (a + b) in equations (i)/(ii), as per convenience of solving.

Thus, substituting in equation (ii), we get

a + b + y = 2a

⇒ y = 2a – a – b

⇒ y = a – b

Hence, we have x = (a + b) and y = (a – b).