Definition of a Time Invariant System: A system is called time invariant if for any input x(t) and any time t_0, the response to x(t-t_0) is also shifted by the same t_0, thus producing y(t-t_0).
Definition of a Time Variant System: A system is called time variant if for any input x(t) and time t_0, the response to x(t-t_0) is not shifted by the same t_0.
