Because the sum of the |m-2| power of the equation set {3x-y = 1} and the 2n+m power of (m+ 1) x =-2 is a binary linear equation set about x and y,

So: |m-2|-2= 1 and m+2n= 1 and m+ 1≠0,

From |m-2|-2= 1: |m-2|=3, m=5 or m=- 1, and m+ 1≠0, so m=5,

Substituting m+2n= 1 gives: 5+2n= 1, and the solution gives n=-2.

Therefore: m=5, n=-2.