|x-2|=7-|y-5|≥0
解得4≤y≤12
|x-2|=y-6≥0
解得y≥6
则,6≤y≤12
|x-2|=7-|y-5|,|x-2|=y-6
则,7-|y-5|=y-6
7-y+5=y-6
2y=18
解得y=9
|x-2|=y-6=9-6=3
x-2=±3
得x=5或x=-1
综上,方程组的解为x=5,y=9或x=-1,y=9