Đáp án:
$\begin{array}{l}
1)m = 1\\
\Rightarrow \left\{ \begin{array}{l}
- 2x + y = 5\\
x + 3y = 1
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
- 2x + y = 5\\
2x + 6y = 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
7y = 7\\
x = 1 - 3y
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1\\
x = - 2
\end{array} \right.\\
\Rightarrow \left( {x;y} \right) = \left( { - 2;1} \right)\\
2)\left\{ \begin{array}{l}
- 2mx + y = 5\\
mx + 3y = 1
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
- 2mx + y = 5\\
2mx + 6y = 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
7y = 7\\
mx + 3y = 1
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1\\
mx = - 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1\\
x = \dfrac{{ - 2}}{m}\left( {m \ne 0} \right)
\end{array} \right.\\
x - y = 2\\
\Rightarrow \dfrac{{ - 2}}{m} - 1 = 2\\
\Rightarrow \dfrac{{ - 2}}{m} = 3\\
\Rightarrow m = - \dfrac{2}{3}\left( {tmdk} \right)\\
3)M\left( {\dfrac{{ - 2}}{m};1} \right)
\end{array}$
Do ta luôn có y=1 nên điểm M luôn nằm trên đt y=1 khi m thay đổi.
