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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. 9X5Y=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 stepbystep. 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 xyplane.

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. 

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