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 August 17th, 2012, 10:33 AM #1 Newbie   Joined: Aug 2012 Posts: 5 Thanks: 0 2 Variable Equation I have an equation that I need to solve for 2 variables. 9X-5Y=3 I have read up on it alot, and I guess I need to pick a variable, isolate it and then continue from there; as follows. 9X=3+5Y 9X/9 = (3+5Y)/9 X = 0.3333 + 0.5556Y Then from here I am supposed to insert it into the first equation. But I dont get the answers the expected. In this paticular equation, X=2 and Y=3. But those are not the answers I get. Can someone explain to me and show me how to solve this paticular equation step-by-step. It would be greatly appreciated. Thanks in advance  August 17th, 2012, 11:10 AM #2 Senior Member   Joined: Feb 2012 Posts: 628 Thanks: 1 Re: 2 Variable Equation You cannot solve one equation in two variables for a unique solution. It is true that one of the solutions to this equation is x = 2, y = 3, but there are infinitely many solutions, as this equation represents a line in the xy-plane. August 17th, 2012, 03:10 PM #3 Newbie   Joined: Aug 2012 Posts: 5 Thanks: 0 Re: 2 Variable Equation Well then can you tell me what to do to solve this? Do we need to make 2 equations? August 17th, 2012, 05:05 PM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: 2 Variable Equation Are you listening? There is NO unique solution. Here's a few (X,Y): 2,3 7,12 12,21 17,30 negatives also: -3,-6 -8,-15 August 17th, 2012, 06:20 PM #5 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: 2 Variable Equation As icemanfan stated, the equation you are given represents a line in the Cartesian plane, and any of the infinitude of points on this line will be a solution: Pick any real number to be x, and the point is on the line. You need another equation which intersects the given line at 1 or more locations in order to get a set of unique solutions. August 19th, 2012, 12:48 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2205 As noted above, there's a family of solutions, not just one unique solution. 9X - 5Y = 3 implies Y = (9X - 3)/5 = (3/5)(3X - 1). Choose a value for X, then you can find Y. Equivalently, (X, Y) = (5t/9, t - 3/5). Choose a value for t, then you can find X and Y. When solving for two variables, two equations are usually needed (for a unique solution). One equation might suffice if the variables are required to have integer values. Tags equation, variable Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Bencz Algebra 4 May 4th, 2013 04:14 PM mtayab1994 Algebra 1 May 18th, 2012 03:49 AM Kosta Algebra 2 December 23rd, 2008 03:04 PM mikeduff9 Algebra 3 October 15th, 2007 10:57 AM superbigio Complex Analysis 1 July 17th, 2007 03:44 PM

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