Note: be VERY VERY careful when you do this.
Move the folder into a folder in your home folder.
Next, open Terminal, wait for it to login (a second or two should do)
you'll see Computername:~ $username (bash) or [Computername:~] username% (tcsh).
Either way, type rm -rf and drag the Previous Systems folder to the Terminal window. hit return. It may say "override rw--r-r" (or something like that) and then have a filename. If that happens, hit cmd-period, hit the up arrow once, and then scroll to the beginning of the line (using the left arrow) and add in sudo (space). Hit return and enter your password. Violá, it's gone!
I bet you wish I remember the easier way 😀