Đáp án:
a) m=-41
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
3x + \left( {m - 1} \right)y = 12\\
\left( {m - 1} \right)x + 12y = 24
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{12 - \left( {m - 1} \right)y}}{3}\\
\left( {m - 1} \right)\left( {\dfrac{{12 - \left( {m - 1} \right)y}}{3}} \right) + 12y = 24
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{12 - \left( {m - 1} \right)y}}{3}\\
\dfrac{{\left( {m - 1} \right)\left( {12 - my + y} \right)}}{3} + 12y = 24
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{12 - \left( {m - 1} \right)y}}{3}\\
12m - 12 - {m^2}y + my - y + my + 36y = 72
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{12 - \left( {m - 1} \right)y}}{3}\\
\left( { - {m^2} + 2m + 35} \right)y = 84 - 12m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{12\left( {7 - y} \right)}}{{\left( {7 - m} \right)\left( {m + 5} \right)}}\\
x = \dfrac{{12 - \left( {m - 1} \right)y}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{12}}{{m + 5}}\\
x = \dfrac{{12 - \left( {m - 1} \right).\dfrac{{12}}{{m + 5}}}}{3} = \dfrac{{12m + 60 - 12m + 12}}{{3\left( {m + 5} \right)}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{12}}{{m + 5}}\\
x = \dfrac{{72}}{{3\left( {m + 5} \right)}} = \dfrac{{24}}{{m + 5}}
\end{array} \right.\\
a)DK:m \ne \left\{ { - 5;7} \right\}\\
x + y = - 1\\
\to \dfrac{{24}}{{m + 5}} + \dfrac{{12}}{{m + 5}} = - 1\\
\to \dfrac{{36}}{{m + 5}} = - 1\\
\to m + 5 = - 36\\
\to m = - 41\\
b)Do:x \in Z;y \in Z\\
\to \left\{ \begin{array}{l}
\dfrac{{24}}{{m + 5}} \in Z\\
\dfrac{{12}}{{m + 5}} \in Z
\end{array} \right. \to \dfrac{{12}}{{m + 5}} \in Z\\
\to m + 5 \in U\left( {12} \right)\\
\to \left[ \begin{array}{l}
m + 5 = 12\\
m + 5 = - 12\\
m + 5 = 6\\
m + 5 = - 6\\
m + 5 = 4\\
m + 5 = - 4\\
m + 5 = 3\\
m + 5 = - 3\\
m + 5 = 2\\
m + 5 = - 2\\
m + 5 = 1\\
m + 5 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
m = 7\left( l \right)\\
m = - 17\\
m = 1\\
m = - 11\\
m = - 1\\
m = - 9\\
m = - 2\\
m = - 8\\
m = - 3\\
m = - 7\\
m = - 4\\
m = - 6
\end{array} \right.
\end{array}\)
