Ta có :

\(\left|x\right|+\left|y\right|\le3\)

\(\Leftrightarrow\) Ta có các trường hợp :

TH1 :

\(\left|x\right|+\left|y\right|=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=0\\\left|y\right|=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\) \(\left(tm\right)\)

TH2 :

\(\left|x\right|+\left|y\right|=1\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=0\\\left|y\right|=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=0\\\left[{}\begin{matrix}y=1\\y=-1\end{matrix}\right.\end{matrix}\right.\) \(\left(tm\right)\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=1\\\left|y\right|=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\\y=0\end{matrix}\right.\) \(\left(tm\right)\)

TH3 :

\(\left|x\right|+\left|y\right|=2\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=0\\\left|y\right|=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=0\\\left[{}\begin{matrix}y=2\\y=-2\end{matrix}\right.\end{matrix}\right.\) \(\left(tm\right)\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=2\\\left|y\right|=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\\y=0\end{matrix}\right.\) \(\left(tm\right)\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=1\\\left|y\right|=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\\\left[{}\begin{matrix}y=1\\y=-1\end{matrix}\right.\end{matrix}\right.\) \(\left(tm\right)\)

TH4 : \(\left|x\right|+\left|y\right|=3\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=0\\\left|y\right|=3\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=0\\\left[{}\begin{matrix}y=3\\y=-3\end{matrix}\right.\end{matrix}\right.\) \(\left(tm\right)\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=3\\\left|y\right|=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\\y=0\end{matrix}\right.\) \(\left(tm\right)\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=1\\\left|y\right|=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\\\left[{}\begin{matrix}y=2\\y=-2\end{matrix}\right.\end{matrix}\right.\) \(\left(tm\right)\)

+) \(\Leftrightarrow\left\{{}\begin{matrix}\left|x\right|=2\\\left|y\right|=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\\\left[{}\begin{matrix}y=1\\y=-1\end{matrix}\right.\end{matrix}\right.\) \(\left(tm\right)\)

Vậy =--.