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individual inputs.

In a system that satisfies the homogeneity property, scaling the input always results in scaling the zero-state response by the same factor. In a system that satisfies the additivity property, adding two inputs always results in adding the corresponding two zero-state responses due to the individual inputs.

Mathematically, for a continuous-time system, given two arbitrary inputs

as well as their respective zero-state outputs

then a linear system must satisfy

for any scalar

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