Answer :

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.


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