Đáp án: $m = 2;m = 0$
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
m.x + y = 2m\\
x + y = 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m.x - x = 2m - 1\\
y = 1 - x
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( {m - 1} \right).x = 2m - 1\left( * \right)\\
y = 1 - x
\end{array} \right.\\
\left( * \right) \Leftrightarrow \left\{ \begin{array}{l}
m\# 1\\
x = \dfrac{{2m - 1}}{{m - 1}} \in Z
\end{array} \right.\\
\Leftrightarrow \dfrac{{2m - 1}}{{m - 1}} = \dfrac{{2m - 2 + 1}}{{m - 1}} = 2 + \dfrac{1}{{m - 1}} \in Z\\
\Leftrightarrow \dfrac{1}{{m - 1}} \in Z\\
\Leftrightarrow \left[ \begin{array}{l}
m - 1 = 1\\
m - 1 = - 1
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
m = 2\left( {tmdk} \right)\\
m = 0\left( {tmdk} \right)
\end{array} \right.\\
Vậy\,m = 2;m = 0
\end{array}$