Solve the following pairs of linear equations:

2x + 3y = 2xy, 6x + 12y = 7xy

Given: 2x + 3y = 2xy, 6x + 12y = 7xy

One of the solutions for given pair of equations will be x = 0 and y = 0

But let us find out some other solution as well.

Divide both the equations with xy,

Putting these value in given equations, we get

2b + 3a = 2, 6b + 12a = 7

So, the given equations transforms into linear equation in two variables i.e.

2b + 3a = 2… (i)

6b + 12a = 7….. (ii)

Multiply equation (i) by 3, so

6b + 9a = 6 … (iii)

6b + 12a = 7….. (ii)

Subtract (iii) from (ii),

6b + 12a – 6b – 9a = 7 – 6

⇒ 3a = 1

Putting above value in (ii),

⇒ 2b = 2 – 1