Đáp án: $\left( {x;y} \right) = \left( {40;50} \right);\left( {450; - 360} \right)$
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
x + y = 90\\
\frac{{10}}{x} - \frac{{10}}{y} = \frac{1}{{20}}
\end{array} \right.\left( {x;y \ne 0} \right)\\
\Rightarrow \left\{ \begin{array}{l}
x = 90 - y\\
\frac{1}{x} - \frac{1}{y} = \frac{1}{{200}}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 90 - y\\
\frac{{y - x}}{{xy}} = \frac{1}{{200}}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 90 - y\\
\frac{{y - \left( {90 - y} \right)}}{{y\left( {90 - y} \right)}} = \frac{1}{{200}}\left( 1 \right)
\end{array} \right.\\
\left( 1 \right) \Rightarrow 200\left( {2y - 90} \right) = 90y - {y^2}\\
\Rightarrow {y^2} + 310y - 18000 = 0\\
\Rightarrow \left[ \begin{array}{l}
y = 50\\
y = - 360
\end{array} \right.\left( {tm} \right)\\
\Rightarrow \left[ \begin{array}{l}
y = 50;x = 90 - y = 40\\
y = - 360;x = 90 - y = 450
\end{array} \right.\\
\Rightarrow \left( {x;y} \right) = \left( {40;50} \right);\left( {450; - 360} \right)
\end{array}$
