So if I have 3 equations, 3 unknowns, and I solve and get to 0=0, I know I have infinitely many solutions. If I get like 0=8, it is not solutions?

My question is... if I have no solutions, how do I know if the three planes are parallel or if they intersect pairwise only or if one plane just intersects two parallel planes? How can I tell which situation it is.