# Problems with Solving a System of Three Equations and Excel **URL:** \ **Category:** Factual Questions\ **Created:** [June 16, 2004, 8:36pm UTC](https://boards.straightdope.com/t/problems-with-solving-a-system-of-three-equations-and-excel/250729 "2004-06-16T20:36:49Z")\ **Posts on this page:** 4\ **Page:** 2
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [June 17, 2004, 3:50pm UTC](https://boards.straightdope.com/t/problems-with-solving-a-system-of-three-equations-and-excel/250729/21 "2004-06-17T15:50:18Z")
> [@wolf\_meister](#): > > Damn - I can’t believe I made an input error :smack: Unconsciounable! No one has **ever** made a mistake in this forum before! I know **I** haven’t! :rolleyes: ---
**Author:** ![gregongie](https://avatars.discourse-cdn.com/v4/letter/g/919ad9/32.png) [@gregongie](https://boards.straightdope.com/u/gregongie)\ **Post date:** [June 17, 2004, 5:54pm UTC](https://boards.straightdope.com/t/problems-with-solving-a-system-of-three-equations-and-excel/250729/22 "2004-06-17T17:54:01Z")
The formulas that define the columns are as follows: D=(-7/3)\*A+(4/3) E=(-1/3)\*A+(1/3) F=(8/3)\*A-(2/3) Where A ranges from 0 to 0.5 in steps of 0.01 G is also a function of A, but is much more complicated and rather difficult to describe here, but I can if need be. However, it should not be linear, though in this region it most likely is nearly so. Also, FWIW, I calculated the determinant of the 3x3 matrix with the x,y,z coeffcients in it out by hand and it was something like 1E-7–so, basically zero. Does this mean the system of equations is indeterminate? (or did I goof on the math?) wolf\_meister: Thank you for the generous offer, but that’s far too much to ask you to do–unless, of course, it’s nearly finished, in which case I’ll take it! For those of you who are curious, I’m trying to extract information about the volumes of the various molecular units in a specfic glass system (the Alkali Germinates-- R20-GeO2 – where R is either Cs, Rb, K, Na, or Li). More details upon request. ---
**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\ **Post date:** [June 17, 2004, 9:13pm UTC](https://boards.straightdope.com/t/problems-with-solving-a-system-of-three-equations-and-excel/250729/23 "2004-06-17T21:13:09Z")
> [@gregongie](#): > > The formulas that define the columns are as follows: > D=(-7/3)\*A+(4/3) > E=(-1/3)\*A+(1/3) > F=(8/3)\*A-(2/3) > Where A ranges from 0 to 0.5 in steps of 0.01 > G is also a function of A, but is much more complicated and rather difficult to describe here, but I can if need be. However, it should not be linear, though in this region it most likely is nearly so. > > Also, FWIW, I calculated the determinant of the 3x3 matrix with the x,y,z coeffcients in it out by hand and it was something like 1E-7–so, basically zero. Does this mean the system of equations is indeterminate? (or did I goof on the math?) The formulas above give a noninvertible matrix, for the reasons I described in my previous post: If you subtract the equations generated using A=A[sub]1[/sub] and A=A[sub]2[/sub], then divide by (A[sub]2[/sub]-A[sub]1[/sub])/3, you always get an equation of the form -7x-y+8z=C[sub]12[/sub] This means that you only have two independent equations. If all of the C[sub]ij[/sub] are the same, the system is indeterminate, but if as you say G is nonlinear, most of the C[sub]ij[/sub] are probably different and the system is inconsistent. It looks like you might be trying to infer properties of some three-component stuff for various different proportions of the components (so D+E+F=1). The problem is that you need to look in different directions; you need another parameter besides A. It’s hard to say more without knowing what properties you’re trying to solve for. What are D,E,F,G,x,y,z? ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [June 17, 2004, 11:29pm UTC](https://boards.straightdope.com/t/problems-with-solving-a-system-of-three-equations-and-excel/250729/24 "2004-06-17T23:29:00Z")
**Greg** It is finished so you might as well have it. One important point you should know (and see my posting #20) - you must input correct numbers if you want to get correct answers !!! :smack: I cannot program it for sloppy inputting like a certain wolf\_meister. [Previous page](https://boards.straightdope.com/t/problems-with-solving-a-system-of-three-equations-and-excel/250729.md?page=1)