Question

Solve for x and y:

`x + 6/y = 6, 3x - 8/y = 5 (y ≠ 0)`

Answer 1

The given equations are:

`x + 6/y = 6`   ...(i)

`3x - 8/y = 5`   ...(ii)

Putting `1/y = v`, we get:

x + 6v = 6   ...(iii)

3x – 8v = 5   ...(iv)

On multiplying (iii) by 4 and (iv) by 3, we get:

4x + 24v = 24   ...(v)

9x – 24v = 15   ...(vi)

On adding (v) from (vi), we get:

13x = 39

⇒ x = 3

On substituting x = 3 in (i), we get:

`3 + 6/y = 6`

⇒ `6/y = (6 - 3)`

⇒ `6/y = 3`

⇒ 3y = 6

⇒ y = 2

Hence, the required solution is x = 3 and y = 2.