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`= 1
Putting x = 1 in (iii), we have
3 × 1 + 2y = 9 ⇒ y = `(9−3)/2`= 3
Hence, x = 1 and y = 3.