If we have the system x(t) and it gives the output y(t), then the system is linear if you can multiply the input by any scalar value and the output will be multiplied by the scalar as well. x(t) -> y(t) then ax(t) -> ay(t).
Linear
If the system is 2(x(t))
If x(t)= sin(t)
x(t) ->[2(x(t))]-> 2(y(t)) or 2*sin(t)
Non-Linear
If the system is $ \int(x(t)) $
If x(t)= $ t^2 $
x(t) ->[$ \int x(t) $]-> (y(t)) or $ t^3 \over 3 $
If the input is multiplied by 1/3 it is not the same as multiplying the output by 1/3
