Ta xét 4TH:
-TH1: \(x\ge-2,y\ge5\)
\(\Rightarrow\left\{{}\begin{matrix}x+y=8\\\left|x+2-y\right|=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=8-x\\\left|x+2-8+x\right|=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=8-x\\\left|2x-6\right|=0\end{matrix}\right.\)\(\left\{{}\begin{matrix}x=3\\y=5\end{matrix}\right.\)(TM)
Vậy x=3; y=5.
-TH2: \(x\ge-2,y< 5\)
\(\Rightarrow\left\{{}\begin{matrix}x-y=-2\\\left|x-y+2\right|=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x-y=-2\\-2+2=0\end{matrix}\right.\)
Vậy hpt có vô số nghiệm với \(x\ge-2,y< 5\) với nghiệm tổng quát \(\left(x\ge-2,x+2\right)\)
-TH3: \(x< -2,y\ge5\)
\(\Rightarrow\left\{{}\begin{matrix}-x-2+y-5=5\\x+2-y=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}-x+y=12\\x-y=-2\end{matrix}\right.\)
Vì \(\dfrac{a}{a'}=\dfrac{b}{b'}\ne\dfrac{c}{c'}\) nên hpt vô nghiệm.
-TH 4: \(x< -2,y< 5\)
\(\Rightarrow\left\{{}\begin{matrix}-x-2-y=0\\x-y=-2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x+y=-2\\x-y=-2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=0\end{matrix}\right.\)(KTM)
Vậy hpt vô nghiệm.
