Could you please tell me what cause my upstairs bathroom to back up into my basement bathroom?

There is blockage in your drain after the basement bathroom. When the upstairs drains it can go through the drain enough so it backs up. Are your drains vented as they should be? I'd start rodding the drain at the nearest cleanout. Maybe remove the toilet in the basement if that doesn't help and rod from there. Check your vent pipe to be sure they are operating correctly.