Question

Solve the following pair of equations by reducing them to a pair of linear equations:

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2,\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

• A. $x=1,y=4$
• B. $x=3,y=2$
• C. $x=4,y=9$
• D. $x=16,y=25$

Answer 1

The correct option is C $x=4,y=9$

Let us put $\frac{1}{\sqrt{x}}=u\&\frac{1}{\sqrt{y}}=v$.

Then the equations become

$2u+3v=2$ ......(i) and

$4u-9v=-1$ .....(ii)

Multiplying (i) by $2$ and subtracting the result from (ii),

$-15v=-5$

$\Rightarrow v=\frac{1}{3}$

So, $\frac{1}{\sqrt{y}}=\frac{1}{3}$

$\Rightarrow y=9$

Again, putting $v=\frac{1}{3}$ in $\left(i\right)$,

$2u+3\times \frac{1}{3}=2$

$\Rightarrow u=\frac{1}{2}$ i.e. $\frac{1}{\sqrt{x}}=\frac{1}{2}$

$\Rightarrow x=4.$

So, $(x,y)=(4,9)$

Hence, option C is correct.