Solve the following system of equations by elimination method:

5x + 3y = 19xy

7x – 2y = 8xy

Given pair of linear equations is

5x + 3y = 19xy …(i)

And 7x – 2y = 8xy …(ii)

On multiplying Eq. (i) by 2 and Eq. (ii) by 3 to make the coefficients of y equal, we get the equation as

10x + 6y = 38xy …(iii)

And 21x – 6y = 24xy …(iv)

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

10x + 6y + 21x – 6y = 38xy + 24xy

⇒ 31x = 62xy

On putting in Eq. (ii), we get

7x – 2y = 8xy

⇒ 7x – 1 = 4x ⇒ – 1 = 4x – 7x

⇒ – 1 = – 3x

On putting x = 0 , we get y = 0

Hence, and , which is the required solution.