Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
a.\left\{ \begin{array}{l}
y = mx - 2\\
3x + m\left( {mx - 2} \right) = 5
\end{array} \right. \to \left\{ \begin{array}{l}
y = mx - 2\\
3x + {m^2}x - 2m = 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = mx - 2\\
x = \frac{{5 + 2m}}{{3 + {m^2}}}
\end{array} \right. \to \left\{ \begin{array}{l}
x = \frac{{5 + 2m}}{{3 + {m^2}}}\\
y = \frac{{5m + 2{m^2} - 6 - 2{m^2}}}{{3 + {m^2}}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \frac{{5 + 2m}}{{3 + {m^2}}}\\
y = \frac{{5m - 6}}{{3 + {m^2}}}
\end{array} \right.
\end{array}\)
⇒ ∀m Hpt luôn có nghiệm
b.
\(\begin{array}{l}
\left\{ \begin{array}{l}
x = \frac{{5 + 2m}}{{3 + {m^2}}} > 0\\
y = \frac{{5m - 6}}{{3 + {m^2}}} < 0
\end{array} \right. \to \left\{ \begin{array}{l}
3 + {m^2} > 0\left( {ld} \right)\forall m \in R\\
5 + 2m > 0\\
5m - 6 < 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m > \frac{{ - 5}}{2}\\
m < \frac{6}{5}
\end{array} \right.\\
\to \frac{{ - 5}}{2} < m < \frac{6}{5}
\end{array}\)
