a: \(\left\{{}\begin{matrix}4x-\left|y+2\right|=3\\x+2\left|y+2\right|=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}8x-2\left|y+2\right|=6\\x+2\left|y+2\right|=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=9\\x+2\left|y+2\right|=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\2\left|y+2\right|=3-1=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\\left|y+2\right|=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y+2\in\left\{1;-1\right\}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\y\in\left\{-1;-3\right\}\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}2\left|x-1\right|+3y=9\\5\left|x-1\right|-2y=-6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4\left|x-1\right|+6y=18\\15\left|x-1\right|-6y=-18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}19\left|x-1\right|=0\\2\left|x-1\right|+3y=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left|x-1\right|=0\\3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-1=0\\y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\y=3\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}x-3\left|5-y\right|=-1\\2x-5\left|5-y\right|=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-6\left|5-y\right|=-2\\2x-5\left|5-y\right|=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-\left|5-y\right|=-2\\2x=5\left|5-y\right|\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left|y-5\right|=2\\2x=5\cdot2=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y-5\in\left\{2;-2\right\}\\x=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y\in\left\{7;-3\right\}\\x=5\end{matrix}\right.\)
