Question

\(\left\{{}\begin{matrix}x-3\left|5-y\right|=-1\\2x-5\left|5-y\right|=0\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x-3\left|5-y\right|=-1\\2x-5\left|5-y\right|=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2x-6\left|y-5\right|=-2\\2x-5\left|y-5\right|=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-\left|y-5\right|=-2\\2x=5\left|y-5\right|\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\left|y-5\right|=2\\2x=5\cdot2=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\\y-5\in\left\{2;-2\right\}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=5\\y\in\left\{7;3\right\}\end{matrix}\right.\)