Question

Solve the following pair of linear equations.

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$

$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

Here, x > 0 and y > 0.

• A. x = 9, y = 8
• 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 given pair of equations is not linear. We will assume $\frac{1}{x}$ is $u^2$ and $\frac{1}{y}$ is $v^2$ then we will get the equation as

$2u+3v=2$

$4u-9v=-1$

We will use method of elimination to solve the equations.
On multiplying the first equation by 3 and we get

$6u+9v=6$

and we have equation (2) i.e. $4u-9v=-1$

Adding the above two equations, we get

$10u=5$

$\Rightarrow u=\frac{1}{2}$

Substituting $u$ in equation $4u-9v=-1$ we get $v=\frac{1}{3}$

Now $x=\frac{1}{u^2}=\frac{1}{(\frac{1}{2}{)}^2}=4$

Similarly, $y=\frac{1}{v^2}=\frac{1}{(\frac{1}{3}{)}^2}=9$