**Linear System**

A system is said to be linear if superposition principle is applicable to the system.

**Superposition Principle**

The response resulting from several input signals can be computed as the sum of the responses resulting from each input signal acting alone. Let x_{1}(t) and x_{2}(t) be the two inputs. The corresponding responses/output are y_{1}(t) and y_{2}(t).

Then the system is linear i.e. follows the principle of superposition if

- The response to x
_{1}(t) + x_{2}(t) is y_{1}(t) + y_{2}(t). This is called**Additivity property**. - The response to ax
_{1}(t) is y_{1}(t), where a is any arbitrarily constant. This is called**Scaling or homogeneity property.**

For Continuous time system: ax_{1}(t) + bx_{2}(t) → ay_{1}(t) + by_{2}(t).

For Discreate time system: ax_{1}(n) + bx_{2}(n) → ay_{1}(n) + by_{2}(n).

When a system violates either the principle of superposition or the property of homogeneity, the system is said to be **nonlinear.**

**Non-Linear System**

A system is said to be non-linear if superposition principle or the property of homogeneity is not applicable to the system.

For a linear system, an input that is zero for all time results in an output that is zero all time. If x(t) → y(t), then homogeneity property tells us that

0 = 0* x(t) → 0* y(t) = 0