solving equations using Excel

[arnold_charming]

Hi!

I want to use Excel to solve an equation. How to do this and with which tools? Below is my equation.

y = 0,75y + 0,4x
x = 0,25y + 0,6x
1 = y + x

I need the value of y and x. Please help me out. Tnx.

Ps: Sorry for duplicating posts, but just now I noticed that this group is more suited then General.

[MrShorty]

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.

[arnold_charming]

Hi!

Thank you.