Time Invariance
A system is time invariant if a shift in the input signal produces the same shift in the output signal. A simple way to check for time invariance is to test whether you can switch the order of the time delay and system operation. If so, the system if time invariant.
Examples
A time invariant system is $ y(t) = 5*x(t)\, $
If you shift the input by a constant, $ x(t-t0)\, $, then the output is $ y(t) = 5*x(t-t0)\, $
A time variant system is $ y(t) = x(3t)\, $
Shifting the input $ x(t-t0)\, $ will yield $ y(t) = x(3*t-t0)\, $
However, if the time is shifted after multiplying the input by 3, the result is $ y(t) = x(3*(t-t0))\, $
Since the two outputs don't match, the system is time variant.
