Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
y = 2 - 2mx\\
x + 2m\left( {2 - 2mx} \right) = 4 - 4m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 2 - 2mx\\
x + 4m - 4{m^2}x = 4 - 4m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 2 - 2mx\\
x = \frac{{4 - 8m}}{{1 - 4{m^2}}} = \frac{{4\left( {1 - 2m} \right)}}{{\left( {1 - 2m} \right)\left( {1 + 2m} \right)}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 2 - 2mx\\
x = \frac{4}{{1 + 2m}}
\end{array} \right.\\
\to y = 2 - 2m.\frac{4}{{1 + 2m}} = \frac{{2 + 4m - 8m}}{{1 + 2m}}\\
= \frac{{2 - 4m}}{{1 + 2m}} = \frac{{ - \left( {4m + 2} \right) + 4}}{{1 + 2m}} = - 2 + \frac{4}{{1 + 2m}}\\
Do:x \in Z;y \in Z\\
\to \left( {1 + 2m} \right) \in U\left( 4 \right)\\
\to \left[ \begin{array}{l}
1 + 2m = 4\\
1 + 2m = - 4\\
1 + 2m = 2\\
1 + 2m = - 2\\
1 + 2m = 1\\
1 + 2m = - 1
\end{array} \right. \to \left[ \begin{array}{l}
m = \frac{3}{2}\left( l \right)\\
m = \frac{{ - 5}}{2}\left( l \right)\\
m = \frac{1}{2}\left( l \right)\\
m = \frac{{ - 3}}{2}\left( l \right)\\
m = 0\left( {TM} \right)\\
m = - 1\left( {TM} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
m = 0\\
m = - 1
\end{array} \right.
\end{array}\)