Đáp án: (x;y)=(4;3)
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
\frac{y}{2} - \frac{{x + y}}{5} = 0,1\\
\frac{y}{5} - \frac{{x - y}}{2} = 0,1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
\frac{{5y - 2\left( {x + y} \right)}}{{10}} = \frac{1}{{10}}\\
\frac{{2y - 5\left( {x - y} \right)}}{{10}} = \frac{1}{{10}}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
5y - 2x - 2y = 1\\
2y - 5x + 5y = 1
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
3y - 2x = 1\left( 1 \right)\\
7y - 5x = 1
\end{array} \right.\\
\Rightarrow 3y - 2x - \left( {7y - 5x} \right) = 0\\
\Rightarrow 3x - 4y = 0\\
\Rightarrow x = \frac{4}{3}y\,\,thay\,vao\,\left( 1 \right)\\
\Rightarrow 3y - 2.\frac{{4y}}{3} = 1\\
\Rightarrow y = 3 \Rightarrow x = \frac{4}{3}y = 4\\
Vậy\,\left( {x;y} \right) = \left( {4;3} \right)
\end{array}$
