Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2$
$\frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$

(X=4, Y=9) Let $\frac{1}{\sqrt{x}} = p$ and $\frac{1}{\sqrt{y}} = q$.
Substituting these into the given equations,we obtain:
$2p + 3q = 2$ $...(1)$
$4p - 9q = -1$ $...(2)$
To eliminate $q$,multiply equation $(1)$ by $3$:
$6p + 9q = 6$ $...(3)$
Adding equation $(2)$ and $(3)$:
$(4p - 9q) + (6p + 9q) = -1 + 6$
$10p = 5$
$p = \frac{5}{10} = \frac{1}{2}$
Substitute $p = \frac{1}{2}$ into equation $(1)$:
$2(\frac{1}{2}) + 3q = 2$
$1 + 3q = 2$
$3q = 1$
$q = \frac{1}{3}$
Now,solve for $x$ and $y$:
$p = \frac{1}{\sqrt{x}} = \frac{1}{2} \implies \sqrt{x} = 2 \implies x = 4$
$q = \frac{1}{\sqrt{y}} = \frac{1}{3} \implies \sqrt{y} = 3 \implies y = 9$
Thus,the solution is $x = 4, y = 9$.