We have,

⇒ bx + ay = 2ab …(i)

ax – by = a² – b²…(ii)

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

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

Recalling equations 1 & 2,

bx + ay = 2ab [×b

ax – by = a² – b² [×a

⇒ b²x + a²x = 2ab² + a³ – ab²

⇒ (b² + a²)x = a (2b² + a² – b²)

⇒ (b² + a²)x = a(b² + a²)

⇒ x = a

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

Thus, substituting in equation (i), we get

ab + ay = 2ab

⇒ ay = 2ab – ab = ab

⇒ y = b

Hence, we have x = a and y = b.