Question

Solve the following pair of equations:

`4x + 6/y = 15, 6x - 8/y = 14, y ≠ 0`

Answer 1

Given pair of linear equations are

`4x + 6/y` = 15  ......(i)

And `6x - 8/y = 14, y ≠ 0`  ....(ii)

Let u = `1/y`, then above equation becomes

4x + 6u = 15   .....(iii)

And 6x – 8u = 14  .....(iv)

On multiplying equation (iii) by 8 and equation (iv) by 6 and then adding both of them, we get

32x + 48u = 120

36x – 48u = 84

⇒ 68x = 204

⇒ x = 3

Now, put the value of x in equation (iii), we get

4 × 3 + 6u = 15

⇒ 6u = 15 – 12

⇒ 6u = 3

⇒ u = `1/2`

⇒ `1/y = 1/2`  .....`[because u = 1/y]`

⇒ y = 2

Hence, the required values of x and y are 3 and 2, respectively.