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August 17th, 2012, 10:33 AM   #1
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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
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August 17th, 2012, 11:10 AM   #2
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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.
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August 17th, 2012, 03:10 PM   #3
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Re: 2 Variable Equation

Well then can you tell me what to do to solve this? Do we need to make 2 equations?
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August 17th, 2012, 05:05 PM   #4
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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
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August 17th, 2012, 06:20 PM   #5
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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.
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August 19th, 2012, 12:48 AM   #6
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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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