Question

If `2/x + 3/y = 9/(xy)` and `4/x +  9/y = 21/(xy)`, find the values of x and y.

Answer 1

The given pair of equation is

`2/x + 3/y = 9/(xy)`   ...(i)

` 4/x + 9/y  = 21/(xy)`  ...(ii)

Multiplying (i) and (ii) by xy, we have

3x + 2y = 9   ...(iii)

9x + 4y = 21   ...(iv)

Now, multiplying (iii) by 2 and subtracting from (iv), we get

9x – 6x = 21 – 18

⇒ `x = 3/3`

⇒ x = 1

Putting x = 1 in (iii), we have

3 × 1 + 2y = 9

⇒ `y = (9 - 3)/2`

⇒ y = 3

Hence, x = 1 and y = 3.