Given, 2/x + 3/y = 9/xy

=> (2y + 3x)/xy = 9/xy

=> 2y + 3x = 9  ...............1

and 4/x + 9/y = 21/xy

=> (4y + 9x)/xy = 21/xy

=> 4y + 9x = 21  .............2

Multiply by 2 in equation 1 and subtract it from equation 2, we get

      2(2y + 3x) - (4y + 9x) = 9 * 2 - 21

=> 4y + 6x - 4y - 9x = 18 - 21

=> -3x = -3

=> x = 1

From equation 1,

      2y + 3 * 1 = 9

=> 2y + 3 = 9

=> 2y = 9 - 3

=> 2y = 6

=> y = 6/2

=> y = 3

So, x = 1, y = 3