Đáp án:
a) m=-1
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x = \dfrac{{12 - \left( {m - 1} \right)y}}{3}\\
\left( {m - 1} \right).\dfrac{{12 - \left( {m - 1} \right)y}}{3} + 12y = 24\left( 1 \right)
\end{array} \right.\\
\left( 1 \right) \to \dfrac{{12m - 12 - \left( {{m^2} - 2m + 1} \right)y}}{3} + 12y = 24\\
\to 12m - 12 - {m^2}y + 2my - y + 36y = 72\\
\to \left( { - {m^2} + 2m + 35} \right)y = 84 - 12m\\
\to \left( {m - 7} \right)\left( {m + 5} \right)y = 12\left( {7 - m} \right)\\
\to y = - \dfrac{{12\left( {m - 7} \right)}}{{\left( {m - 7} \right)\left( {m + 5} \right)}} = - \dfrac{{12}}{{m + 5}}\\
\to x = \dfrac{{12 - \left( {m - 1} \right)\left( { - \dfrac{{12}}{{m + 5}}} \right)}}{3}\\
= \dfrac{{12m + 60 + 12m - 12}}{{3\left( {m + 5} \right)}}\\
= \dfrac{{24m + 48}}{{3\left( {m + 5} \right)}} = \dfrac{{8m + 16}}{{m + 5}}\\
a)DK:m \ne - 5\\
Do:x + y = - 1\\
\to \dfrac{{8m + 16}}{{m + 5}} - \dfrac{{12}}{{m + 5}} = - 1\\
\to 8m + 4 = - m - 5\\
\to 9m = - 9\\
\to m = - 1\\
b)Do:x = \dfrac{{8m + 16}}{{m + 5}} = \dfrac{{8\left( {m + 5} \right) - 24}}{{m + 5}}\\
= 8 - \dfrac{{24}}{{m + 5}}\\
y = - \dfrac{{12}}{{m + 5}}\\
Do:x;y \in Z\\
\to \left\{ \begin{array}{l}
\dfrac{{24}}{{m + 5}} \in Z\\
\dfrac{{12}}{{m + 5}} \in Z
\end{array} \right.\\
\to \dfrac{{12}}{{m + 5}} \in Z\\
\to m + 5 \to U\left( {12} \right)\\
\to \left[ \begin{array}{l}
m + 5 = 12\\
m + 5 = - 12\\
m + 5 = 6\\
m + 5 = - 6\\
m + 5 = 2\\
m + 5 = - 2\\
m + 5 = 1\\
m + 5 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
m = 7\\
m = - 17\\
m = 1\\
m = - 11\\
m = - 3\\
m = - 7\\
m = - 4\\
m = - 6
\end{array} \right.
\end{array}\)
