At first I had trouble proving the time variance for this as I would do the usual mistake as in question Is the system represented by the equation $y(t) = x(2t)$ time invariant?. The solution has graphical representation of all the shifts in the process and they are the following.
I get the shift from the first picture to the second. It gets compressed, I know that property. I also understand what happens in the third picture. The $x_1(t)$signal is shifted to the right because of $t-2$ . The fifth picture is fine as well, it's just a shift to the right again from the second picture.
What I'm having trouble with is the 4th picture. I know that $y_2(t)=x_2(t)=x_1(2t-t_0)$ I forgot to mention, all the graphs are for $t_0=2$.
- Shouldn't the 4th picture be a shift of 2 to the right?
- And the last one maybe $(2t-2t_0)$ so $2t_0=4$ units to the right?