Đáp án:
\(m < - \dfrac{{223}}{{36}}\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
3x + 6y = 3m + 9\\
4x - 6y = 2m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
7x = 5m + 9\\
y = \dfrac{{2x - m}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5m + 9}}{7}\\
y = \dfrac{{2x - m}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5m + 9}}{7}\\
y = \dfrac{{2.\dfrac{{5m + 9}}{7} - m}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5m + 9}}{7}\\
y = \dfrac{{10m + 19 - 7m}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5m + 9}}{7}\\
y = \dfrac{{3m + 19}}{3}
\end{array} \right.\\
Có:x + y < - 3\\
\to \dfrac{{5m + 9}}{7} + \dfrac{{3m + 19}}{3} < - 3\\
\to \dfrac{{15m + 27 + 21m + 133 + 21.3}}{{21}} < 0\\
\to 36m + 223 < 0\\
\to m < - \dfrac{{223}}{{36}}
\end{array}\)
