I do not back up my Apps or System Files.
If you select your System directory to exclude, you get the option to exclude all "system" files. This makes it so that only data that is not in /System /Library or /Applications is backed up by Time Machine. I also have it excluding ~/Downloads and ~/Library. This is because I have a Macbook Pro and have it set up to operate off of the main disk and then use an rsync script to sync my backup to a colocated server that I have.
This allows me to keep everything running well.