Đáp án:
$\begin{array}{l}
a)Thay\,\left( {x;y} \right) = \left( { - 2;3} \right)\,vào\,hpt:\\
\left\{ \begin{array}{l}
- 2 + 3.m = 4\\
n.\left( { - 2} \right) + 3 = - 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
m = 2\\
n = 3
\end{array} \right.\\
b)\left\{ \begin{array}{l}
x + my = 4\\
nx + y = - 3
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
nx + mny = 4n\\
nx + y = - 3
\end{array} \right.\\
\Rightarrow mny - y = 4n - \left( { - 3} \right)\\
\Rightarrow \left( {mn - 1} \right).y = 4n + 3\\
Có\,vô\,số\,nghiệm \Leftrightarrow \left\{ \begin{array}{l}
mn - 1 = 0\\
4n + 3 = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
mn = 1\\
n = - \frac{3}{4}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
m = \frac{{ - 4}}{3}\\
n = - \frac{3}{4}
\end{array} \right.
\end{array}$
