Does my system support 3TB hard drives?

What you want to do is go to disk management and see.
Right click on computer and select manage then next select disk management , when your in disk management you will see all the drives that are connected to your computer and once you get there you may be greeted with a screen that says your drive needs to be initialized, if so that will be your 3 tb drive. Just follow the prompts to select create new partiotion and then fromat and give the new drive a drive letter.
If your not greeted by that screen then look in the list of drives listed and see if one of them says raw unallocated space and right click on it and do the same as I just wrote .