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 $x>0,y>0)$

• A. $x=9,y=4$
• B. $x=4,y=9$
• C. $x=3,y=2$
• D. $x=\frac{1}{2},y=\frac{1}{3}$

Answer 1

The correct option is B

$x=4,y=9$

The pair of equations is not linear.
We will substitute $\frac{1}{x}$ as $u^2$ and $\frac{1}{y}$ as $v^2$. (As $x>0andy>0)$
Then we will get the equations as
$2u+3v=2$ ...(i)
$4u-9v=-1$ ...(ii)
We will use method of elimination to solve the above equations.
On multiplying the first equation by 3, we get
$6u+9v=6$ ...(iii)
On adding the equations (ii) and (iii), we get
$6u+9v=6$
$4u-9v=-1$
___________
$u=\frac{1}{2}$
Substituting the value of u in equation (i), we get
$v=\frac{1}{3}$
So $x=\frac{1}{u^2}=4$ and $y=\frac{1}{v^2}=9$.