A system is call linear if the system is "distributive".
system(input1+input2)=system(input1)+system(input2)
Ex. The system is y(t)=2x(t+3).
The output of the signal x1(t)=t is y1(t)=2(t+3)=2t+6. The output of the signal x2(t)=t-1 is y2(t)=2(t+3-1)=2t+4.
What is the output of the signal x(t)=x1(t)+x2(t)=t+t-1?
y(t)=2(2(t+3)-1)=2(2t+5)=4t+10
This system is linear beacause
y(t)=4t+10 y1(t)+y2(t)=2t+6+2t+4=4t+10
