How to delete "system" storage?

You don't. System is the space taken up by the Operating System. Its what makes your computer work. If you delete that, then the computer stops working.

Free up storage space on your Mac - Apple Support

Basically no, the files in the System category are part of macOS Sierra operating system. You will also notice that when you choose the Manage option on the Storage tab, both the Other Users and System options are grayed out.

On a commonsense level, I agree that you should avoid deleting System files unless you really know what you're doing. That said, your System storage allocation is huge. As of today, Apple still sells a MacBook Air with 128GB of storage, and there's an expectation on that machine that a 'clean' System will take up somewhere between 8GB-13GB. So how/why are you using 80GB+ more than that? There are many reasons, but I'd start with:

• uninstalling any old/unused applications, using actual uninstallers or referring to the developers' websites for instructions
• this isn't a machine that is rarely rebooted, correct?
• how many full OS X version updates have you done on this machine?
• you're not a graphic designer/font hoarder, are you?
• DaisyDisk is a great space analyzer that can help target where chunks of possibly deletable files are located (or at least give a clue to why you're short on space)

There is also the nuclear option, which is a Clean Install. That would take some planning (multiple good backups, application installers, etc.), but it would get you back to the most streamlined version of Sierra it could be.