\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{4}{5}\\\dfrac{1}{x}-\dfrac{1}{y}=\dfrac{1}{5}\end{matrix}\right.\left(x,y\ne0\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{4}{5}\\\dfrac{1}{x}+\dfrac{1}{x}=\dfrac{4}{5}+\dfrac{1}{5}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{4}{5}\\\dfrac{2}{x}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{2}+\dfrac{1}{y}=\dfrac{4}{5}\\x=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{1}{\dfrac{4}{5}-\dfrac{1}{2}}\\x=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{10}{3}\\x=2\end{matrix}\right.\)
