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Solving Simultaneous Equations

David is facing the task of solving some simultaneous equations in Excel, most with ten variables or more. He asked if there were some resources he could reference that would be good for learning how to do this.

Working with simultaneous equations is not for the mathematically faint-of-heart. The easiest way to solve simultaneous equations is to use matrix math, which is built into Excel. Such tasks are definitely not in the realm of simple mathematics, and a full discussion of simultaneous equations would be beyond the scope of ExcelTips. There are, however, several good resources you can use to help bring you up to speed. The following three sites have been suggested as starting points by other ExcelTips subscribers:

http://www.duncanwil.co.uk/simult.html
http://educ.jmu.edu/~drakepp/spreadsheet/howto/matrices.pdf
http://homepage1.nifty.com/gfk/renritu-excel-e.htm

If you prefer to use printed books instead of online resources, you might try Guide to Microsoft Excel 2002 for Scientists and Engineers (ISBN 0750656131) in which simultaneous equations are addressed beginning on page 210. While this book is obviously for an older version of Excel, the techniques relative to simultaneous equations are still applicable to later versions of Excel. In fact, you could visit Amazon and simply search for "simultaneous equations" (with the quotes) and find a good number of potential sources for detailed information.

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (3079) applies to Microsoft Excel 97, 2000, 2002, and 2003.

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Comments for this tip:

John Markey    14 Jun 2014, 10:42
Another good hint: Before you publish an article to the world is to check that it is error free. The second formula shown in the referenced "edu.jmu.edu" link should read "a-2c=0" and not "a-c=0". The matrix also represents "a-c=0". In the Excel example the author did use the correct formula and representation, otherwise an error would have occurred.
Bill Tastle    07 Jun 2014, 09:55
An excellent tip, and one that is easy to understand. And, it seems to me, not at all that mathematically "advanced." If one can add and multiply, one has already learned the concepts necessary to learn matrix manipulation, at least to the level presented here. This is something every business person should be able to do. What may be the harder part of this activity is the identification of equations from the real world.
 
 

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