\(\left\{{}\begin{matrix}2\left|x-6\right|+3\left|y+1\right|=5\\5\left|x-6\right|-4\left|y+1\right|=1\end{matrix}\right.\)
Đặt u=|x-6|;v=|y+1| ta có hệ phượng trình :
\(\left\{{}\begin{matrix}2u+3v=5\\5u-4v=1\end{matrix}\right.< =>\left\{{}\begin{matrix}u=1\\v=1\end{matrix}\right.\)
Thay u=1 v=1 ta có
\(\left\{{}\begin{matrix}1=\left|x-6\right|\\1=\left|x+1\right|\end{matrix}\right.< =>\left\{{}\begin{matrix}x-6=\pm1\\y+1=\pm1\end{matrix}\right.< =>\left\{{}\begin{matrix}\left[{}\begin{matrix}x=7\\x=5\end{matrix}\right.\\\left[{}\begin{matrix}y=0\\y=-2\end{matrix}\right.\end{matrix}\right.\)
Vậy hệ pt có nghiệm (x,y) là ( 7;0);(7;-2);(5;0);(5;-2)
