Question

Solve for x and y:

`5/x - 3/y = 1, 3/(2x )+ 2/(3y) = 5 (x ≠ 0, y ≠ 0)`

Answer 1

The given equations are:

`5/x - 3/y = 1`  ...(i)

`3/(2x) + 2/(3y) = 5`   ...(ii)

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

5u – 3v = 1   ...(iii)

⇒ `3/2 u + 2/3 v = 5`

⇒ `(9u + 4v)/6 = 5`

⇒ 9u + 4v = 30   ...(iv)

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

20u – 12v = 4   ...(v)

27u + 12v = 90   ...(vi)

On adding (iv) and (v), we get:

47u = 94 ⇒ u = 2

⇒ `1/x = 2 ⇒ x = 1/2`

On substituting `x = 1/2` in (i), we get:

`5/(1/2) - 3/y = 1`

⇒ `10 - 3/y = 1`

⇒ `3/y = (10 - 1)`

⇒ `3/y = 9`

`y = 3/9`

`y = 1/3`

Hence, the required solution is `x = 1/2` and `y = 1/3`.