When was your home built?
What type of pipe is the waste line? PVC, Cast iron, Copper?
2" solid matter can't cause a stoppage in a 4" line normaly.
You could have a belly in the line or it may have been a fluke.
Modern toilets should not back up a drain line if they are in good shape and the pitch is correct.
If you are very concerned you can have someone with a camera come and you can have the line inspected for problems, about $200.00 or so.