Question

Solve for x and y:

`9/x - 4/y = 8, (13)/x + 7/y = 101 (x ≠ 0, y ≠ 0)`

Answer 1

The given equations are:

`9/x - 4/y = 8`   ...(i)

`(13)/x + 7/y = 101`   ...(ii)

Putting `1/x = u` and `1/y = v`, we get:

9u – 4v = 8   ...(iii)

13u + 7v = 101   ...(iv)

On multiplying (iii) by 7 and (iv) by 4, we get:

63u – 28v = 56   ...(v)

52u + 28v = 404   ...(vi)

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

115u = 460 ⇒ u = 4

⇒ `1/x = 4 ⇒ x = 1/4`

On substituting `x = 1/4` in (i), we get:

`9/(1/4) - 4/y = 8`

⇒ `36 - 4/y = 8`

⇒ `4/y= (36 - 8)`

⇒ `4/y = 28`

`y = 4/28`

`y = 1/7`

Hence, the required solution is `x = 1/4` and `y = 1/7`.