I have two bathrooms on the same three inch drain line. One is on the second floor, the other on the first. There is a vent up out the roof. When the upstairs toilet is flushed, the first floor toilet splashes out. This systems has worked fine until just recently. What is the problem and what can I do to fix it?

Most likely there's a partial clog in the drain pipe downstream of the 1st floor toilet. It may need to be cleared with a pipe cleaning machine. Depending on the cleanouts and their whereabouts, the toilet may need to be removed.

Thank you. I have a cleanout in the basement. I will try my 50 ft hand snake on it.

I understood you to say it was bubbling, only the first floor and only when you flush the 2nd floor.

I would check the venting also. If the sewer line is obscured that may be contributing to the problem, but bubbling.... Normally flushing a 2nd floor would cause captured air to be released through this venting. So even if the sewer were draining but slowly the captured air has an escape route outside the home. If the venting is blocked, or constricted/obscured, then the captured air seeks another exit (your downstairs toilet--bubbling). The problem is that the gasses are detrimental to your health if inhaled over time so it's a good idea to check the venting as well. I had a bird who decided to build a nest on top of one of my vents. Then apparently decided to move.