Đáp án:
$\begin{array}{l}
1b)\left\{ \begin{array}{l}
\left( {x + 2} \right)\left( {y - 3} \right) = \left( {x + 1} \right)\left( {y + 2} \right)\\
3x - 2y = 5
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
xy - 3x + 2y - 6 = xy + 2x + y + 2\\
3x - 2y = 5
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
5x - y = - 8\\
3x - 2y = 5
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
10x - 2y = - 16\\
3x - 2y = 5
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
7x = - 21\\
y = 5x + 8
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 3\\
y = 5.\left( { - 3} \right) + 8 = - 7
\end{array} \right.\\
Vậy\,\left( {x;y} \right) = \left( { - 3; - 7} \right)\\
2)\left\{ \begin{array}{l}
mx + y = 3\\
x + 2y = 2
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2mx + 2y = 6\\
x + 2y = 2
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
2mx - x = 6 - 2\\
y = \dfrac{{x - 2}}{2}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( {2m - 1} \right).x = 4\left( * \right)\\
y = \dfrac{{x - 2}}{2}
\end{array} \right.
\end{array}$
Hệ pt có nghiệm duy nhất khi pt (*) có nghiệm duy nhất
$\begin{array}{l}
\Leftrightarrow 2m - 1 \ne 0\\
\Leftrightarrow m \ne \dfrac{1}{2}\\
Vậy\,m \ne \dfrac{1}{2}
\end{array}$
