Recently on my Ubuntu 16.04 LTS, I encountered error "System is running in low-graphics mode" and there is no way you can login or proceed beyond this error screen.
For me this happened when I renamed
/usr/share/X11/xorg.conf.d directory while I was trying to solve one of the graphics related problems.
On the error window, press ctrl+alt+f3 to get to the console. Here the filesystem is mounted but in read-only mode so you can't edit to rename the directory back for correction.
To mount the filesystem in read-write mode, use following command
mount -o rw,remount /
It would mount the filesystem in read-write mode. Now you can correct the name of the directory using
mv command. Then, use
exit command and Press Alt + → multiple times till you get to the UI again.
If required, reboot the system using
reboot command, now you should be able to login as usual.