Definition
If Z(t) and W(t) in the following are equal the system is linear.
Examples
Linear:
An example of an linear function is $ \ y(t) = 3x(t + 8) $
because the result of the 1st method above yields $ \ 3ax(t + 8) + 3bx(t + 8) $
and the result of the 2nd method above yields $ \ 3[ax(t + 8) + bx(t + 8)] $. Because they yield the same result the system is linear.
Non-Linear:
An example of a non-linear function is $ \ y(t) = e^{x(t)} $
because the result of the 1st method above yields $ \ e^{ax(t)} + e^{bx(t)} $
and the result of the 2nd method above yields $ \ e^{ax(t) + bx(t)} $, which is not equal to the first result.
