Đáp án: $m = - 3$
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
x + my = 3\\
2x - \left( {m + 1} \right).y = 4
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2x + 2my = 6\\
2x - \left( {m + 1} \right).y = 4
\end{array} \right.\\
\Leftrightarrow 2x + 2my - 2x + \left( {m + 1} \right).y = 6 - 4\\
\Leftrightarrow \left( {2m + m + 1} \right).y = 2\\
\Leftrightarrow \left( {3m + 1} \right).y = 2\\
\Leftrightarrow \left\{ \begin{array}{l}
3m + 1\# 0\\
y = \dfrac{2}{{3m + 1}}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m\# - \dfrac{1}{3}\\
y = \dfrac{2}{{3m + 1}}
\end{array} \right.\\
Do:x + my = 3\\
\Leftrightarrow x = 3 - my\\
= 3 - \dfrac{{2m}}{{3m + 1}}\\
= \dfrac{{9m + 3 - 2m}}{{3m + 1}} = \dfrac{{7m + 3}}{{3m + 1}}\\
Khi:x + y = 2\\
\Leftrightarrow \dfrac{{7m + 3}}{{3m + 1}} + \dfrac{2}{{3m + 1}} = 2\\
\Leftrightarrow \dfrac{{7m + 5}}{{3m + 1}} = 2\\
\Leftrightarrow 7m + 5 = 6m + 2\\
\Leftrightarrow m = - 3\left( {tmdk:m\# - \dfrac{1}{3}} \right)\\
Vậy\,m = - 3
\end{array}$
