My Math Forum Solve This Equation For xy

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 June 13th, 2018, 08:08 AM #1 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 632 Thanks: 85 Solve This Equation For xy 3x^2 + xy = 2y^2 Can you solve for xy?
 June 13th, 2018, 09:37 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond Hi EvanJ. $$3x^2 + xy = 2y^2$$ $$3x^2+xy-2y^2=0$$ $$(3x-2y)(x+y)=0\implies 3x=2y,x=-y$$ $$3x^2=2xy$$ $$xy=-y^2$$ Now sub into the original equation and take it from there. Thanks from EvanJ
 June 13th, 2018, 10:25 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,950 Thanks: 987 Using quadratic: solve for x : x = -y or x = 2y/3 solve for y : y = -x or y = 3x/2 Just trying to cause confusion
June 13th, 2018, 04:48 PM   #4
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Quote:
 Originally Posted by greg1313 $$(3x-2y)(x+y)=0\implies 3x=2y,x=-y$$
The left hand equation doesn't imply that both right hand equations hold.

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