if determinant of that is than sys have unique solution ....

Edit:

1° when and if at least one of than solutions are unique and given

2° if and if at least one of than system of equations have no solutions

3° if and if than there can be :

a) all sub determinants of D are zeros, and coefficients with the unknowns are proportional there are 2 cases :

- all independent members of system are proportional with coefficient with unknowns than there are infinity of solutions

- all independent members of system are not proportional with coefficient with unknowns than there are no solutions

b) if at least one sub determinant of D are different from zero than there are infinity of solution