Đáp án:
\(\left[ \begin{array}{l}
m = 2\\
m = 4\\
m = 6\\
m = 8\\
m = 10\\
...
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x + y = m + 2\\
3x + 5y = 2m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3x + 3y = 3m + 6\\
3x + 5y = 2m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
2y = - m - 6\\
x = m + 2 - y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{ - m - 6}}{2}\\
x = m + 2 - \dfrac{{ - m - 6}}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{ - m - 6}}{2}\\
x = \dfrac{{2m + 4 + m + 6}}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{3m + 10}}{2} = \dfrac{{3m}}{2} + 5\\
y = \dfrac{{ - m - 6}}{2} = - \dfrac{m}{2} - 3
\end{array} \right.\\
Do:x \in Z;y \in Z\\
\to \left\{ \begin{array}{l}
\dfrac{{3m}}{2} \in Z\\
\dfrac{m}{2} \in Z
\end{array} \right.\\
\to \dfrac{m}{2} \in Z\\
\to m \in B\left( 2 \right)\\
\to \left[ \begin{array}{l}
m = 2\\
m = 4\\
m = 6\\
m = 8\\
m = 10\\
...
\end{array} \right.
\end{array}\)
