Can I hook the drain pipe for the washer into the drain pipe for the bathroom sink(2" pipe)?

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Can I hook the drain pipe for the washer into the drain pipe for the bathroom sink(2" pipe)?

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If you are on a septic tank the answer is no. If you are on city sewer the answer is yes you can, however, I can see problems on down the line. If you do. Where the plan. I connecting the drain? Before or after the lavatory Trap? Please explain how you intend to hook all this up? Let me know, Tom