Đáp án:
$\begin{array}{l}
\left( I \right):\left\{ \begin{array}{l}
x - y = 1\\
4x + 5y = 17
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
4x - 4y = 4\\
4x + 5y = 17
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
9y = 13\\
x = 1 + y
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = \dfrac{{13}}{9}\\
x = 1 + \dfrac{{13}}{9} = \dfrac{{22}}{9}
\end{array} \right.\\
\Rightarrow \left( {x;y} \right) = \left( {\dfrac{{22}}{9};\dfrac{{13}}{9}} \right)\\
\Rightarrow \left( {II} \right)\left\{ \begin{array}{l}
m.\dfrac{{22}}{9} + n.\dfrac{{13}}{9} = 6\\
3m.\dfrac{{22}}{9} + 2n.\dfrac{{13}}{9} = 10
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
22m + 13n = 54\\
33m + 13n = 45
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
11m = - 9\\
13n = 45 - 33m
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
m = \dfrac{{ - 9}}{{11}}\\
n = \dfrac{{72}}{{13}}
\end{array} \right.\\
Vậy\,m = \dfrac{{ - 9}}{{11}};n = \dfrac{{72}}{{13}}
\end{array}$
