Đáp án:
\(\dfrac{6}{{25}} > m > - 3\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
2x + 3y = m\\
25x - 3y = 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
27x = m + 3\\
2x + 3y = m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{m + 3}}{{27}}\\
y = \dfrac{{m - 2x}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{m + 3}}{{27}}\\
y = \dfrac{{m - 2.\dfrac{{m + 3}}{{27}}}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{m + 3}}{{27}}\\
y = \dfrac{{27m - 2m - 6}}{{81}} = \dfrac{{25m - 6}}{{81}}
\end{array} \right.\\
Do:x > 0;y < 0\\
\to \left\{ \begin{array}{l}
\dfrac{{m + 3}}{{27}} > 0\\
\dfrac{{25m - 6}}{{81}} < 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m + 3 > 0\\
25m - 6 < 0
\end{array} \right.\\
\to \dfrac{6}{{25}} > m > - 3
\end{array}\)
