You have 3 equations in 3 unknowns. Geometrically, this means that the 3 planes coincide and that those values of x,y,z that satisfy the equation ax+b+z=0, automatically satisfy all three equations. Most of the times, a system with the same number of equations and unknowns has a single unique solution. By the way, we say that a linear system is homogeneous if its constant term is zero!