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Linearity

A system is said to be linear if it satisfies the properties of scaling and superposition. Thus, the following holds true for all linear systems:

Suppose there are two inputs
$ \,x1(t) $
$ \,x2(t) $
with outputs
$ \,y1(t) = C\left\{x1(t)\right\} $
$ \,y2(t) = C\left\{x2(t)\right\} $
A linear system must satisfy the condition
$ \,ay1(t) + by2(t) = C\left\{ax1(t) + bx2(t)\right\} $

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