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The question posted would be an inappropriate question for GMAT database because - in GMAT questions, the information given in statements can never contradict each other ever
but as per your question, Statement 1: xy > 0 contradicts with Statement 2) x > 0 and y < 0 which means xy<0
So you might want to correct the mistake. However the underlying concept of finding integer solutions to a linear equation is good one to discuss on this forum.
Also, please read the rules of posting question on forum and follow them while posting a question because the heading of question is inappropriate for users to sort when required.
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