Đáp án:
$\begin{array}{l}
a)n = - 3\\
\Rightarrow \left\{ \begin{array}{l}
- 3x - y = 5\\
2x - 9y = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
- 6x - 2y = 10\\
6x - 27y = 21
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
- 29y = 31\\
2x - 9y = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = - \dfrac{{31}}{{29}}\\
x = \dfrac{{9y + 7}}{2} = \dfrac{{ - 38}}{{29}}
\end{array} \right.\\
Vậy\,\left( {x;y} \right) = \left( {\dfrac{{ - 38}}{{29}};\dfrac{{ - 31}}{{29}}} \right)\\
2)\left\{ \begin{array}{l}
nx - y = 5\\
2x + 3my = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
2nx - 2y = 10\\
2nx + 3mny = 7n
\end{array} \right.\\
\Rightarrow \left\{ {3mny + 2y = 7n - 10} \right.\\
\Rightarrow \left( {3mn + 2} \right).y = 7n - 10\left( * \right)
\end{array}$
Để hệ pt có nghiệm thì pt (*) có nghiệm
$\begin{array}{l}
\Rightarrow 3mn + 2 \ne 0\\
\Rightarrow m.n \ne - \dfrac{2}{3}
\end{array}$
