I live in Aurora Colorado I live in a duplex and my basement shower is backing up anytime we flush the tolet, the other unit is dry could all the rain we have received be causing this?

Not unless you are on septic but then why would the other one work? Sounds like a blockage in your line before the main drain and before the other unit drain.

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my basement shower is backing up anytime we flush the tolet

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You have a blockage downstream from the toilet. The solution would be to pull the toilet and snake. The main drain. Good luck, Tom