Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
x + y = m\\
2x - my = 0
\end{array} \right.\\
1)m = - 1\\
\Leftrightarrow \left\{ \begin{array}{l}
x + y = - 1\\
2.x - \left( { - 1} \right).y = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x + y = - 1\\
2x + y = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2x + y - x - y = 0 - \left( { - 1} \right)\\
y = - 1 - x
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 1\\
y = - 2
\end{array} \right.\\
Vậy\,x = 1;y = - 2\,khi:m = - 1\\
2)a)x = 1;y = 1\\
\Leftrightarrow \left\{ \begin{array}{l}
1 + 1 = m\\
2.1 - m = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m = 2\\
m = 2
\end{array} \right.\\
Vậy\,m = 2\\
b)\left\{ \begin{array}{l}
x + y = m\\
2x - my = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2x + 2y = 2m\\
2x - my = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2y + my = 2m\\
x = m - y
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( {m + 2} \right).y = 2m\left( * \right)\\
x = m - y
\end{array} \right.
\end{array}$
Hệ pt vô nghiệm thì pt * vô nghiệm
$\begin{array}{l}
\Leftrightarrow \left\{ \begin{array}{l}
m + 2 = 0\\
2m\# 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m = - 2\\
m\# 0
\end{array} \right.\\
Vậy\,m = - 2\\
3)\left\{ \begin{array}{l}
\left( {m + 2} \right).y = 2m\\
x = m - y
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m\# - 2\\
y = \dfrac{{2m}}{{m + 2}}\\
x = m - y = m - \dfrac{{2m}}{{m + 2}} = \dfrac{{{m^2}}}{{m + 2}}
\end{array} \right.\\
Vậy\,\left( {x;y} \right) = \left( {\dfrac{{{m^2}}}{{m + 2}};\dfrac{{2m}}{{m + 2}}} \right)\,khi:m\# - 2\\
4)m\# - 2\\
x + y = 1\\
\Leftrightarrow m = 1\left( {do:x + y = m} \right)\left( {tm} \right)\\
Vậy\,m = 1
\end{array}$
