A system that, for an input consisting of the sum of a number of signals, produces an output that is the sum, or superposition, of the system’s response to each input considered separately. For example, if the input waveform x1[t] to a system produces the output y1[t] and the input x2[t] produces the output y2[t], then the system is linear if the output is {y1[t] + y2[t]} when the input applied is {x1[t] + x2[t]}.
A linear system will also produce a weighted sum of outputs if the inputs are so weighted, such that an input of {ax1[t] + bx2[t]} will produce an output of {ay1[t] + by2[t]}, where a and b are constants.