Question

Solve the following pair of equations :
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$ and $\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1.$

Answer 1

Let

$\begin{array}{c}\frac{1}{\sqrt{x}}=\alpha ,\frac{1}{\sqrt{y}}=\beta \\ 2\alpha +3\beta =2\left[1\times 2\right]\\ \underset{–}{4\alpha -9\beta =-1}\\ 15\beta =5\\ \Rightarrow \beta =\frac{1}{3}\\ 2\alpha =2-1\\ 2\alpha =1\\ \Rightarrow \alpha =\frac{1}{2}\\ \frac{1}{\sqrt{y}}=\frac{1}{3}\\ \Rightarrow y=9\\ \frac{1}{\sqrt{x}}=\frac{1}{2}\\ \Rightarrow x=4\end{array}$

Hence, this is the answer.