Superposition Principle

The superposition principle states that the response of a linear system to a sum of multiple inputs is the sum of the responses to each input separately. In other words, if a system is linear, it satisfies the principle of superposition. This principle is widely used in physics and engineering to analyze and solve problems involving linear systems.

A function $F(x)$ that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties: 

additivity

$$F(x_1+x_2)=F(x_1)+F(x_2)$$

and homogeneity

$$F(ax)=aF(x)$$

for a scalar $a$