if one of the pivot elements of the gauss elimination problem is 0 then what will happen to its solutions?
If it is possible to swap that row with a lower one so that the pivot is not 0, then nothing "happens". If it is not then either of two things can happen:
1) If the corresponding "right side" is 0 then there exist an infinite number of solutions.
2) If the corresponding "right side" is not 0 then there is no solution.