We have,

⇒ b²x – a²y + a²b + ab² = 0

⇒ a²y – b²x = a²b + ab² …(i)

bx – ay = - 2ab

⇒ ay – bx = 2ab …(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),

a²y – b²x = a²b + ab²

ay – bx = 2ab [×b]

⇒ a²y – aby = a²b – ab²

⇒ (a² – ab)y = a²b – ab²

⇒ a(a – b)y = ab(a – b)

⇒ y = b

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

Thus, substituting in equation (ii), we get

a(b) – bx = 2ab

⇒ ab – bx = 2ab

⇒ bx = ab – 2ab = - ab

⇒ x = - a

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