This is definitely due to inadequate venting. If it's a single story house,
look to see if there is a vent thru the roof above the affected bath group.
If there is a vent, check to see if there is an obstruction. It is possible
an animal went in there got stuck and died. Or, someone could have
intentionally clogged the vent. People do weird things. Once I went on a
service call to a house with drainage problems an found a tenant had stuffed
potatoes into the drains & vents because he was mad at the landlord. Since
you just bought this place, who knows what happened prior to you buying it.
You can run a garden hose into the vent to see if it flows thru or backs up.
If there is no vent, some method of venting would be required to solve the
problem. If there is no way to add a proper vent, the last resort would be
install an in-line, or so called "mechanical", vent to the drainage system.
These are prohibited by code in most states but sometimes there is no other
alternative when correct venting is not possible.
More info would help in giving more advice.