If i have a system of linear equations in matrix form such as:
1 1 1 1 400
1 -1 0 0 0
0 1 -2 0 0
0 0 1 -10 0
I can solve it using gaussian elimination. However, I am curious about solving such a system if one or more of the variables is an integer. Are there techniques out there to accomplish this and what error are they attempting to reduce?