# Solve for x and y: bx - ay + 2ab = 0.

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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