Are we talking about the right "System"? On my setup if I go to "About This Mac" then select "Storage" then "Manage" the size for "System" is given as 83.96Gb.
But if I right click on the "System" folder under Macintosh HD and choose "Get info" it is only 7.87Gb (the "Library" folder just above is 4.88Gb and "Applications" folder above that 8.01Gb). The largest folder is "Users" which comes to 78.18Gb.
So for me to reduce the 83.96Gb figure as reported by "About This Mac" by any meaningful amount it would require deleting files from within the "User" folder which just happens to store my music, photos, mail etc as well as caches as pointed out by Drew.
What I'm trying to say is just because "On This Mac" reports a certain "System" size it does not mean that is what the actual operating system is taking, that figure is given by /System and /Library (in my case 7.87Gb plus 4.88Gb) which is approx 13Gb, a far cry from the above 83.96Gb figure.
If I'm looking at this correctly then the easiest way for me to reduce the 83.96Gb figure would be to off load music and photos to external storage, but that would make no difference to the 13Gb figure which is purely OS related.