Đáp án: $x = \dfrac{{20}}{{41}};y = - \dfrac{{10}}{{13}}$
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{6}{8} = \dfrac{3}{4}\\
\dfrac{4}{x} + \dfrac{6}{y} = \dfrac{2}{5}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{4}{x} + \dfrac{4}{y} = 3\\
\dfrac{4}{x} + \dfrac{6}{y} = \dfrac{2}{5}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{4}{x} + \dfrac{6}{y} - \dfrac{4}{x} - \dfrac{4}{y} = \dfrac{2}{5} - 3\\
\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{3}{4}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{2}{y} = \dfrac{{ - 13}}{5}\\
\dfrac{1}{x} = \dfrac{3}{4} - \dfrac{1}{y}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{1}{y} = \dfrac{{ - 13}}{{10}}\\
\dfrac{1}{x} = \dfrac{{41}}{{20}}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{20}}{{41}}\\
y = - \dfrac{{10}}{{13}}
\end{array} \right.\\
Vậy\,x = \dfrac{{20}}{{41}};y = - \dfrac{{10}}{{13}}
\end{array}$
