Question

Solve the following pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$
$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
(Where $x>0,y>0)$

Answer 1

The pair of equations are not linear. We will substitute
$\frac{1}{x}$ as $u^2$ and $\frac{1}{y}$ as $v^2$ (As $x>0,y>0)$
Then we will get the equations as
$2u+3v=2$
$4u-9v=-1$
We will use method of elimination to solve the equation
$6u+9v=6$
$4u-9v=-1$
Adding the above two equations
$u=\frac{1}{2}$
Substituting u in above equations, we get $v=\frac{1}{3}$
So $x=\frac{1}{u^2}=4$
$y=\frac{1}{v^2}=9$