Late to the party, but I have the same setup as you (2013 MacBook Pro w/ 120 GB drive). Your "System" files should only take up roughly 20 - 50 GB. 50 if you never cleaned your computer since you bought it, 20 If you have done regular maintenance.
Here are a few steps to fix this problem:
1) Download MacCleaner and use it to remove any unwanted programs from your computer, checking ALL boxes when deleting the program. This will help cut time later.
2) Download the free trail of Daisy Disk. When asked if you would like to purchase, just click "Test Drive". Next to the "Scan" button, click the down arrow, and select "Scan as Administrator" and enter your password in the popup box to start the scan (you only have to enter your password once, required by macOS to access some files).
After the scan is complete, click through the menu on the right hand side to see where your largest files are at. Delete ONLY the files you are sure of. If you are not sure what a file is, GOOGLE IT. If you still are not sure, LEAVE IT.
When you want to delete a file, simply right-click on it in the menu, and select "Show in Finder", then delete it in finder. If it is hidden, it is likely hidden for a reason! If you want to delete a hidden file, you can open terminal and type "defaults write com.apple.finder AppleShowAllFiles YES && killall Finder" to do this. Just make sure to type "defaults write com.apple.finder AppleShowAllFiles NO && killall Finder" to re-hide them when your done!
3) Restart your laptop in safe mode! To do this, restart in which ever manner you wish making sure your sound is at a level you can hear it. When you hear the chime, hold down either SHIFT key. Release it when you see the Apple logo. Login to the first screen. After this, you may restart (without holding the shift) and your space should be restored!
IF your "System" space has not been restored to bellow 35GB, you have a rogue system file!