Đáp án:
$\begin{array}{l}
1)a)Dkxd:\left\{ \begin{array}{l}
x + 5 \ge 0\\
7 - x > 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x \ge - 5\\
x < 7
\end{array} \right.\\
\Rightarrow - 5 \le x < 7\\
b)DKxd:\left\{ \begin{array}{l}
2x + 3 > 0\\
- 2x + 1 \ge 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x > - \frac{3}{2}\\
x \le \frac{1}{2}
\end{array} \right.\\
\Rightarrow - \frac{3}{2} < x \le \frac{1}{2}\\
2)a)\text{pt vô nghiệm}\\
\Rightarrow \Delta ' < 0\\
\Rightarrow {\left( {3m - 1} \right)^2} - 3.\left( {3{m^2} - m + 1} \right) < 0\\
\Rightarrow 9{m^2} - 6m + 1 - 9{m^2} + 3m - 3 < 0\\
\Rightarrow - 3m - 2 < 0\\
\Rightarrow m > - \frac{2}{3}\\
\text{Vậy}\,m > - \frac{2}{3}\\
b)m = 2 > - \frac{2}{3}\\
\Rightarrow \text{pt vô nghiệm}\\
3)\left\{ \begin{array}{l}
3x + a.y = 5\\
2x + y = b
\end{array} \right.\\
\Rightarrow y = b - 2x\\
\Rightarrow 3x + a.\left( {b - 2x} \right) = 5\\
\Rightarrow \left( {3 - 2a} \right).x = 5 - ab\left( 1 \right)
\end{array}$
+ hệ pt vô nghiệm thì pt (1) vô nghiệm
$ \Rightarrow \left\{ \begin{array}{l}
3 - 2a = 0\\
5 - ab \ne 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
a = \frac{3}{2}\\
b \ne \frac{5}{a}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
a = \frac{3}{2}\\
b \ne \frac{{10}}{3}
\end{array} \right.$
+ Hệ pt có 1 nghiệm thì:
$3 - 2a \ne 0 \Rightarrow a \ne \frac{3}{2}$
+ Hệ pt có vô số nghiệm thì:
$\left\{ \begin{array}{l}
3 - 2a = 0\\
5 - ab = 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
a = \frac{3}{2}\\
b = \frac{5}{a} = \frac{{10}}{3}
\end{array} \right.$
