Solution of $\frac{1}{x}+\frac{1}{y}=2$ and $\frac{1}{x}-\frac{1}{y}=3$ is___________ .

Given equations are, $\frac{1}{x}+\frac{1}{y}=2 and \frac{1}{x}-\frac{1}{y}=3$ 

Let us take, $\frac{1}{x}=p and \frac{1}{y}=q$ 

Then, 

p + q = 2,   ...(1)

and, 

p - q = 3,    ...(2)

Adding (1) and (2) we get, 2p = 5 

 or, $p=\frac{5}{2}$ 

$\Rightarrow x=\frac{1}{p}=\frac{2}{5}$

Subtracting (1) from (2) we get, -2q = 1 

Or, $q=\frac{-1}{2}$ 

$\Rightarrow y=\frac{1}{q}=-2$

Hence, $\mathrm{y}=-2 \mathrm{and} \mathrm{x}=\frac{2}{5}$