In this paper, Beveral sovable classes of linear time-varying systems are identified and explicit methods for finding their solutions are given. It is also shown that any linear time-varying system can be transformed into an algebraically equivalent commutative linear time-varying system or a time-invariant system, provided that an appropriate non-singular (time-varying) algebraic transformation can be found. Consequently it is concluded that the eommutativity of a linear time-varying system is not an inherent property of a dynamic system, but rather is a representation, property.