Solve for x and y :
` ( 2)/(sqrt x ) + (3)/(sqrty ) = 2, ( 4)/(sqrtx ) - ( 9)/(sqrty) = - 1 ( x ne 1, y ne 0 )`

Explanation

Putting ` (1)/(sqrtx ) = u and (1)/(sqrty) = v `, the given equations become
` 2u + 3v = 2 " "`… (i)
` 4u - 9v = - 1 " " ` … (ii) Multiplying (i) by 3 and adding the result with (ii), we get
` 6u + 4u = 6- 1 `
` rArr 10 u = 5`
` rArr u = (5)/(10) rArr u = (1)/(2)`
Putting `u = (1)/(2)` in (i), we get
` ( 2 xx (1)/(2)) + 3v = 2 `
` rArr 1 + 3v = 2 rArr 3 v = 1 rArr v = (1)/(3)`
Now, `u = (1)/(2) rArr (1)/(sqrtx) = (1)/(2) rArr sqrtx = 2 rArr = 2 rArr x = 4`.
And, `v = (1)/(3) rArr (1)/( sqrty ) = (1)/(3) rArr sqrty = 3 rArr y = 9`
Hence, ` x = 4 and x = 9`.