If I try to use
sudo kate to edit a system file, I get the message:
Executing Kate as root is not possible.
So how can I edit a system file?
I put up this question so that I could answer it myself. As far as I can tell, none of the suggestions involving gksudo have any advantage over the solution I proposed: just edit the file as a non-root user, save it when you're done, and provide the root password at that time.