I have the following System with (input x(t), output(y(t)), that I have to check for linearity and time-invariance.
$y(t) = x(t) + \cos(w_o t )$
I am able to show that it is time-variant. For linearity I am not that sure. Here is what I have done so far.
$$ y_1(t)= x_1(t) +\cos(w_0t)\\ y_2(t)= x_2(t) +\cos(w_0t) $$
Adding these give me $y_1(t) + y_2(t) = x_1(t) + \cos(w_0t) +x_2(t) +\cos(w_0t)$
Now $x_1(t) + x_2(t) \rightarrow $ system $\rightarrow x_1(t) + x_2(t) +\cos(w_0t)$.
Is this correct?