Đáp án:
\[\left[ \begin{array}{l}
x = y = 0\\
\left\{ \begin{array}{l}
x = 0\\
y = \pm 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x = \pm 1\\
y = 0
\end{array} \right.
\end{array} \right.\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left| x \right| + \left| y \right| < 2\\
\left| x \right|;\,\left| y \right| \ge 0 \Rightarrow 0 \le \left| x \right|;\left| y \right| < 2\\
x;y \in Z \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
\left| x \right| = 0\\
\left| y \right| = 0
\end{array} \right.\\
\left\{ \begin{array}{l}
\left| x \right| = 0\\
\left| y \right| = 1
\end{array} \right.\\
\left\{ \begin{array}{l}
\left| x \right| = 1\\
\left| y \right| = 0
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = y = 0\\
\left\{ \begin{array}{l}
x = 0\\
y = \pm 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x = \pm 1\\
y = 0
\end{array} \right.
\end{array} \right.
\end{array}\)
