Solve the following system of equations by elimination method:

, where x ≠ 0 and y ≠ 0

Given pair of linear equations is

Or 2x + 5y = 6xy …(i)

And

Or 4x – 5y = – 3xy …(ii)

On adding Eq. (i) and Eq. (ii), we get

2x + 5y + 4x – 5y = 6xy – 3xy

⇒ 6x = 3xy

⇒ y = 2 and x = 0

On putting y = 2 in Eq. (ii), we get

2x + 5(2) = 6xy

⇒ 2x + 10 = 6x(2)

⇒ 2x + 10 = 12x ⇒ 2x – 12x = – 10

⇒ – 10x = – 10

⇒ x = 1

On putting x = 0 , we get y = 0

Hence, x = 0,1 and y = 0,2 , which is the required solution.