Question

Solve for x and y:

`2x - 3/y = 9, 3x + 7/y = 2 (y ≠ 0)`

Answer 1

The given equations are:

`2x - 3/y = 9`   ...(i)

`3x + 7/y = 2`   ...(ii)

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

2x – 3v = 6   ...(iii)

3x + 7v = 2   ...(iv)

On multiplying (iii) by 7 and (iv) by 3, we get:

14x – 21v = 63   ...(v)

9x + 21v = 6   ...(vi)

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

23x = 69 ⇒ x = 3

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

`2 xx 3 - 3/y = 9`

⇒ `6 - 3/y = 9`

⇒ `3/y = -3`

⇒ y = –1

Hence, the required solution is x = 3 and y = –1.