ExcelBanter - solving equations using Excel

Several possible methods for solving a system of linear equations. You
could graph the equations and pick off the point of intersection, or
solve by substitution or elimination. There are several tutorials on
the web for these methods (put "solving systems of linear equations"
into your favorite search engine) and the correct level algebra text
should also describe the techniques.

Implementing them in Excel or any other computer program will be
easiest if you decide on a standard form for the equations (ax+by=c,
y=mx+b, or whatever). Then you build your spreadsheet and you only
need to input the coefficients.

The way I would do it would be to set up as ax+by=c which then can be
expressed by the matrix equation AX=C where A is your coefficient
matrix, X is your unknown matrix, and C is your constant matrix. Then
you can use Excel's built in matrix functions (MINVERSE, MMULT) to
solve the matrix equation X=[A^-1]C. This format is readily extended
to systems of equations in more unknowns.

You will also need to decide how you want the spreadsheet to determine
cases where there are an infinite number of solutions (ie eqn1 and eqn2
represent the same line) or no solutions (ie eqn1 and eqn2 represent
parallel lines).

Also recognize that, due to natural computer round off error, the
algorithm used to generate the inverse matrix can yield slightly
inaccurate results or even garbage, so you'll want to build a little
routine that "checks" the answer by plugging the derived x and y back
into the original equations to make sure a solution has been found.

--
MrShorty
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