Question

Solve for $x$:
$\frac{2}{\sqrt{x}}+\frac{8}{\sqrt{y}}=2$
$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

Answer 1

$\to \frac{2}{\sqrt{x}}+\frac{8}{\sqrt{y}}=2$...(1)

$\frac{4}{\sqrt{x}}+\frac{9}{\sqrt{y}}=-1$....(2)

Eq.$\left(1\right)\times \left(2\right)$

eqn (2) $\Rightarrow \frac{25}{\sqrt{y}}=5\Rightarrow \frac{25}{\sqrt{5}}\Rightarrow y=25$

Putting in (1), $\frac{2}{\sqrt{x}}+\frac{8}{\sqrt{5}}=2\Rightarrow \frac{2}{\sqrt{x}}=2-\frac{8}{5}=\frac{2}{5}\Rightarrow \sqrt{x}=5$

$\Rightarrow x=25$