How to determine if the system is linear or nonlinear Given a signal 

$$y(n)=x(n)\cos(wn)$$

How to determine if the given signal is linear or non linear?

I am getting so confused reading the theory. If someone could help step by step to determine this. It would be great thankyou
As Matt L. says you'll need to check for homogeneity and, possibly, additivity.

Homogeneity

That test says that if:
$$
y[n] = f(x[n])
$$
then
$$
A \cdot y[n] = f(A \cdot x[n])
$$
for all scalar $A$.

Additivity

This test says that if
$$
y_1[n] = f(x_1[n])
$$
and
$$
y_2[n] = f(x_2[n])
$$
then
$$
y_{\rm tot}[n] = f(x_1[n] + x_2[n]) = y_1[n] + y_2[n]
$$

You just need to apply these for your system.



I say "possibly" because if the system fails one of these tests, then it will not be linear --- so there is little point testing the second condition.