Đáp án:
$\begin{array}{l}
1)\left\{ \begin{array}{l}
9x + y = 11\\
5x + 2y = 9
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
18x + 2y = 22\\
5x + 2y = 9
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
13x = 13\\
y = 11 - 9x
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 1\\
y = 2
\end{array} \right.\\
Vậy\left( {x;y} \right) = \left( {1;2} \right)\\
2)\\
a)m = 3\\
\Leftrightarrow {x^2} - 10x + {3^2} + 3.3 - 2 = 0\\
\Leftrightarrow {x^2} - 10x + 16 = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {x - 8} \right) = 0\\
\Leftrightarrow x = 2/x = 8\\
Vậy\,x = 2;x = 8khi\,m = 3\\
b)\Delta ' > 0\\
\Leftrightarrow {\left( {m + 2} \right)^2} - {m^2} - 3m + 2 > 0\\
\Leftrightarrow {m^2} + 4m + 4 - {m^2} - 3m + 2 > 0\\
\Leftrightarrow m > - 6\\
Theo\,Viet:\left\{ \begin{array}{l}
{x_1} + {x_2} = 2\left( {m + 2} \right)\\
{x_1}{x_2} = {m^2} + 3m - 2
\end{array} \right.\\
A = 2018 + 3{x_1}{x_2} - x_1^2 - x_2^2\\
= 2018 + 5{x_1}{x_2} - \left( {x_1^2 + x_2^2 + 2{x_1}{x_2}} \right)\\
= 2018 + 5.\left( {{m^2} + 3m - 2} \right) - {\left( {{x_1} + {x_2}} \right)^2}\\
= 2018 + 5{m^2} + 15m - 10 - 4\left( {{m^2} + 4m + 4} \right)\\
= 5{m^2} + 15m + 2008 - 4{m^2} - 16m - 16\\
= {m^2} - m + 1992\\
= {\left( {m - \dfrac{1}{2}} \right)^2} + \dfrac{{7967}}{4} \ge \dfrac{{7967}}{4}\\
\Leftrightarrow A \ge \dfrac{{7967}}{4}\\
\Leftrightarrow GTNN:A = \dfrac{{7967}}{4}\\
Khi:m = \dfrac{1}{2}\left( {tmdk} \right)\\
Vậy\,m = \dfrac{1}{2}
\end{array}$
