We have,

⇒ bx + ay = a²b + ab² …(i)

b²x + a²y = 2a²b²…(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 a, so that variable y in both the equations have same coefficient.

Recalling equations (i) & (ii),

bx + ay = a²b + ab² [×a

b²x + a²y = 2a²b²

⇒ abx – b²x = a³b – a²b²

⇒ b(a – b)x = a²b(a – b)

⇒ x = a²

Substitute x = a² in equations (i)/(ii), as per convenience of solving.

Thus, substituting in equation (i), we get

b(a²) + ay = a²b + ab²

⇒ a²b + ay = a²b + ab²

⇒ ay = ab²

⇒ y = b²

Hence, we have x = a² and y = b².