A system is time invariant if for any time shifted input signal the system produces a shifted output such that if an input $ x(t) $ produced an output $ y(t) $ then the input $ x(t + t_0) $ would produced the output $ y(t + t_0) $
Time invariant Signal
$ S_1(t) = 5t $ $ S_2(t) = t - t_0 $
$ x(t) -> S_1(t) $ $ s_1(t) = 5t $
