\(\left\{{}\begin{matrix}2x+5\left|y-1\right|=2\\x-2\left|y-1\right|=1\end{matrix}\right.\)
\(\left\{{}\begin{matrix}4x+10\left|y-1\right|=4\\5x-10\left|y-1\right|=5\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x=1\\x-2\left|y-1\right|=1\end{matrix}\right.\)
\(\Leftrightarrow\left|y-1\right|=0\Rightarrow y=1\)