Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
mx + y = 7\\
2x - y = - 4
\end{array} \right.\\
\Rightarrow mx + y + 2x - y = 7 - 4\\
\Rightarrow \left( {m + 2} \right)x = 3\\
\Rightarrow x = \frac{3}{{m + 2}}\left( {m \ne - 2} \right)\\
\Rightarrow y = 2x + 4 = 2.\frac{3}{{m + 2}} + 4 = \frac{{4m + 14}}{{m + 2}}\\
\Rightarrow P = {x^2} + {y^2}\\
P = \frac{9}{{{{\left( {m + 2} \right)}^2}}} + \frac{{{{\left( {4m + 14} \right)}^2}}}{{{{\left( {m + 2} \right)}^2}}}\\
P = \frac{{16{m^2} + 112m + 205}}{{{m^2} + 4m + 4}}\\
\Rightarrow \left( {P - 16} \right){m^2} + \left( {4P - 112} \right)m + 4P - 205 = 0\\
\Rightarrow \Delta ' = {\left( {2P - 56} \right)^2} - \left( {P - 16} \right).\left( {4P - 205} \right) \ge 0\\
\Rightarrow 4{P^2} - 224P + 3136 - 4{P^2} + 269P - 3280 \ge 0\\
\Rightarrow 45P \ge 144\\
\Rightarrow P \ge \frac{{16}}{5}\\
\Rightarrow GTNN:P = \frac{{16}}{5} \Leftrightarrow m = - \frac{{31}}{8}
\end{array}$
