How do I show if this system is time-varying?
In order to show that a system is time-varying, it is sufficient to find one counter-example, where the response to a shifted input signal does not equal a shifted version of the original output signal.

In your case you might want to consider the signal

$$x(t)=\begin{cases}&amp;1,&amp; 0&lt;t&lt;1\\
&amp;-1,&amp; -1&lt;t&lt;0\\
&amp;0,&amp;\text{otherwise}\end{cases}$$

Now try to figure out the corresponding output signal $y(t)$. Next, take a shifted version of $x(t)$, e.g. $x(t-1)$, as the input signal and see what output signal you get. Is it equal to $y(t-1)$? If not, you've just shown that the system is indeed time-varying.