Solve the following system of equations by elimination method:

x + y = 7xy

2x – 3y = – xy

Given pair of linear equations is

x + y = 7xy …(i)

And 2x – 3y = – xy …(ii)

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

2x + 2y = 14xy …(iii)

On subtracting Eq. (ii) and Eq. (iii), we get

2x + 2y – 2x + 3y = 14xy + xy

⇒ 2y + 3y = 15xy

⇒ 5y = 15xy

On putting in Eq. (ii), we get

2x – 3y = – xy

On putting x = 0 , we get x = 0

Hence, and , which is the required solution.