Đáp án:
\(\left[ \begin{array}{l}
m = 3\\
m = - 5\\
m = 1\\
m = - 3\\
m = - 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
mx + y = 3m - 1\\
{m^2}x - y = m + 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {{m^2} + m} \right)x = 4m\\
{m^2}x - y = m + 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m\left( {m + 1} \right)x = 4m\\
y = {m^2}x - m - 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{4}{{m + 1}}\left( {DK:m \ne \left\{ { - 1;0} \right\}} \right)\\
y = \dfrac{{4{m^2} - {m^2} - m - m - 1}}{{m + 1}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{4}{{m + 1}}\\
y = \dfrac{{3{m^2} - 2m - 1}}{{m + 1}}
\end{array} \right.\\
Do:x \in Z\\
\to \dfrac{4}{{m + 1}} \in Z\\
\to m + 1 \in U\left( 4 \right)\\
\to \left[ \begin{array}{l}
m + 1 = 4\\
m + 1 = - 4\\
m + 1 = 2\\
m + 1 = - 2\\
m + 1 = 1\\
m + 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
m = 3\\
m = - 5\\
m = 1\\
m = - 3\\
m = 0\left( l \right)\\
m = - 2
\end{array} \right.\\
Thay:\left[ \begin{array}{l}
m = 3\\
m = - 5\\
m = 1\\
m = - 3\\
m = - 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = 5\\
y = - 21\\
y = 0\\
y = - 16\\
y = - 15
\end{array} \right.\\
KL:\left[ \begin{array}{l}
m = 3\\
m = - 5\\
m = 1\\
m = - 3\\
m = - 2
\end{array} \right.
\end{array}\)
