Can I add a washer and connect to drain under a sink?

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asr9754

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santa maria, CA
I have a utility sink. Id like to put a clothes washer in the next room along the same wall. My question, can i punch thru the wall with some piping and connect the drainage from the washer to the existing drain lines under the sink?
Bad drawing attached. Hoping for any advice if this is possible/safe. Thanks,!
 

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