Michael Kwayisi

Simultaneous (System of) Equations Solver

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System of equations solver based on the Gaussian algorithmSystem of equations solver based on the Gaussian algorithm

This is an online simultaneous equations solver (otherwise known as a system of equations solver) based on the Gaussian elimination algorithm. This equations solver can solve up to several hundred equations of unknowns! To use it, type the full equations in the text area below, each on a separate line, then click on the Solve button to trigger the solving process. After the results have been calculated, they will appear just below the text area. In addition to showing you the solution, the solver will attempt to show you how it understood your equations. For example, typing in an equation like 0x + 1y + 2z = 3 will simply show as y + 2z = 3.

This simultaneous equations solver was meant to be just a proof-of-concept implementation to corroborate the fact that, it is feasible to develop an equations solver that can parse a given set of equations, extract the required data, and solve for theoretically an unlimited number of unknowns, thus freeing the user from any complexity. However, shortly after appearing online, it attracted so much widespread usage that I decided to keep it, even though I have no immediate plans to update it. Because of this historical design philosophy, unconventional equations and carelessly formed equations with unnecessary constants will fail to parse.

NOTE: The parser for this simultaneous equations solver expects all input equations to be in the form ax ± by [...] = c where a, b, and c are integers, and x and y are unknowns. Because of the very limited support for different syntaxes, equations where the constant appears before the equals sign will fail to parse correctly. Moreover, equations that are in the form c = x (a) + y (b), c = x * a + y * b, c = xa + yb, or even xa + yb = c, where, in all the aforementioned equations, x and y are the unknowns, a and b are coefficients, and c is a constant, will result in an error. To solve such an equation, first convert it into the form ax + by = c before passing it to the solver.

The source code of this simultaneous equations solver is available for your reading pleasure :)

Comments (10)

  1. HamzahHamzah
    May 5, 2015 20:21 GMT

    Thanks dude
    really helped me out although it could include some proper working out
    still don't know what's going on in Maths
    you saved my aaaaaaaaassssssssssssssssssss

  2. samuelsonsamuelson
    Nov 16, 2014 08:48 GMT

    Fantastic however could have proper working out.

    1. Michael KwayisiMichael Kwayisi
      Mar 27, 2015 11:53 GMT

      Samuelson, Gaylord: Thanks for your feedback. Actually, I'm planning to develop an all-equations solver that can solve all sorts of mathematical statements and show working as well. If you've got some additional ideas, don't hesitate to let me know.

  3. Philip PaulonePhilip Paulone
    Feb 12, 2017 06:14 GMT

    You should include the word linear in your description since I cannot input variables to a power greater than 1

  4. Eilishmacall@gmail.comEilishmacall@gmail.com
    Oct 22, 2015 15:00 GMT

    How do you put in fractions?:

    y= 1/4x + 1/2
    y= 2x - 10

    Doesn't work please help!!

    1. Michael KwayisiMichael Kwayisi
      Oct 22, 2015 16:54 GMT

      Eilish, unfortunately you can't put in (common) fractions at this time; you'd have to resolve them to decimals instead. So your equations should have been inputted as such:

      y - 0.25x = 0.5
      y - 2x = -10

    Jul 21, 2015 02:50 GMT

    Thanks for the instant answers for 9 eq'ns & 9 unknowns. Besides, I need the step by step process. Anyway, thanks a lot.

  6. Hamzah(again!!)Hamzah(again!!)
    May 5, 2015 20:31 GMT

    Not so good news this time
    tried this:
    .......................and its DONT WORK!
    Comes up with this rubbish:
    Character 'd' in equation 2 at offset 5.



    1. Michael KwayisiMichael Kwayisi
      May 6, 2015 08:20 GMT

      Hamzah, your equations are actually three:
      1) 7c + 5d = -16
      2) -6c = 25
      3) 7d = 25
      If they are actually all true, you only need to input just any 2 of them :)

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