LINEARITY
For a system to be called Linear the following two scenarios must yield output signals that are equal to each other.
1) Signals $ X_1 $ and $ Y_1 $ are first multiplied by constants $ C_1 \in \mathbb{C} $ and $ C_2\in \mathbb{C} $ respectively, then added together and passed through a system that yields a signal $ Z(t) $.
and
2) Signals $ X_1 $ and $ Y_1 $ each pass through a system, their results are multiplied by constants $ C_1 \in \mathbb{C} $ and $ C_2\in \mathbb{C} $ respectively, and then added together yielding a signal $ W(t) $.
For this system to be linear, signals $ Z(t) $ and $ W(t) $ must be equal to each other.
$ Z(t) = W(t) $
