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If you want to do it yourself start by taking a look at the waste water lines in the basement to see if they ALL exit the home from the same pipe or if there are multiple outlet pipes. If there are multiple outlet pipes and they are located away from each other then most likely some fixtures in the home are directed into a grey water dry well; however there are times when an addition has been put on a building the multiple lines may all go into the septic system.
Once you have determined if you have one (or more) exit pipes, determine if the backup is caused by all the fixtures in the home or just some. If there is only ONE exit pipe and only SOME of the fixtures cause a backup then the issue is inside the home and a plumber should be called, if ALL the fixtures cause the backup a septic professional can open the tank and determine if the issue is in the system or the piping to the system. The most common cause of a backup is a “paper jam” from overuse of toilet paper. Never remove the cleanout cap inside your home if you are having a backup- an unpleasant relief of the backup may occur!
If there are Multiple exit pipes try to determine which fixtures are causing the backup and which exit line they tie into. Again, if it is a Single fixture causing the backup the issue is inside the home and a plumber should be called. If it is ALL the fixtures then determine (as best as possible) if that exit pipe leads to the septic system. If the toilets are connected to this line then it is the septic line and a septic professional can open the tank and determine if the issue is in the system or the piping to the system. If the backup occurs in an exit line without any toilets connected to it and it exits the home on a different side than the septic tank is located it is most likely a grey water dry well that is no longer accepting waste water. There are multiple reasons a grey water dry well may stop accepting waste water- crushed/restricted pipes to the dry well, root invasion, or a failed dry well.