Question

giai hpt

\(\left\{{}\begin{matrix}\left|x-1\right|+\left|y-2\right|-1=0\\\left|x-1\right|+y-3=0\end{matrix}\right.\)  

̣

 

Answer 1

Trừ vế cho vế:

\(\left|y-2\right|+2-y=0\Leftrightarrow\left|y-2\right|=y-2\)

\(\Rightarrow y\ge2\)

Mặt khác \(3-y=\left|x-1\right|\ge0\Rightarrow y\le3\)

\(\Rightarrow2\le y\le3\)

\(\Rightarrow0\le3-y\le1\Rightarrow0\le\left|x-1\right|\le1\)

\(\Rightarrow-1\le x-1\le1\Rightarrow0\le x\le2\)

Hệ đã cho có vô số nghiệm sao cho:  \(\left\{{}\begin{matrix}0\le x\le2\\2\le y\le3\\\left[{}\begin{matrix}\left|x-1\right|+y-3=0\\\end{matrix}\right.\end{matrix}\right.\)