Define Characteristics of Discrete Time Systems - Linear?

A discrete-time system is said to be linear if it obeys the principles of superposition. That is, the response of a linear system to two or more inputs is equal to the sum of the responses of the system to each input acting separately in the absence of all other inputs. For example, if an input, x₁[n], to the system gives rise to the output, y₁[n], and another input x₂[n] produces the output y [n], the response of the system to both inputs will be

a₁x₁[n] + a₂x₂[n] → a₁y₁[n] + a₂y₂[n]  

Where a₁ and a₂ are arbitrary constants.