Results 1 to 2 of 2

Math Help - 3 Simultaneous Equations (Possibly Multiple or No Solutions)

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    1

    Post 3 Simultaneous Equations (Possibly Multiple or No Solutions)

    Problem:
    117x+390y+390z=a
    144x+216y+384z=b
    260x+520y+45z=c

    x, y & z are all positives integers.

    What are all the possible values for x, y & z?
    Values of a, b & c are not important.

    --

    Hi, I studied both Calculus & Statistics in high school but that's it. In my statistics class I learnt about solving these sorts of equations (I believe it actually belongs in Algebra) but those equations were simpler because a, b & c were known. Also, I learnt something about graphing simpler ones to find optimal solutions for situations (Linear Programming).

    Now I believe that with the use of advanced understanding in what would be a 3D version of the 2D "Linear Programming" idea, that those possible values for x, y & z can be easily found. Or found that there is indeed, no solution.

    This is my first post, so please, if I have made a mistake in posting in the wrong section - let me know. Thanks a lot in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by Giorgi View Post
    Problem:
    117x+390y+390z=a
    144x+216y+384z=b
    260x+520y+45z=c

    x, y & z are all positives integers.

    What are all the possible values for x, y & z?
    Values of a, b & c are not important.

    --

    Hi, I studied both Calculus & Statistics in high school but that's it. In my statistics class I learnt about solving these sorts of equations (I believe it actually belongs in Algebra) but those equations were simpler because a, b & c were known. Also, I learnt something about graphing simpler ones to find optimal solutions for situations (Linear Programming).

    Now I believe that with the use of advanced understanding in what would be a 3D version of the 2D "Linear Programming" idea, that those possible values for x, y & z can be easily found. Or found that there is indeed, no solution.

    This is my first post, so please, if I have made a mistake in posting in the wrong section - let me know. Thanks a lot in advance!
    I would recommend that you set these equations up in matrix format and then use some method of solving matrix equations to find the solution.

    Either by a Gaussian elimination or by taking the inverse of the matrix.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 18th 2010, 09:09 AM
  2. Multiple simultaneous equations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 18th 2010, 06:57 AM
  3. Multiple Unknowns in Simultaneous Equations.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 25th 2009, 08:28 AM
  4. Multiple Simultaneous Equations
    Posted in the Algebra Forum
    Replies: 12
    Last Post: October 4th 2009, 07:31 PM
  5. Replies: 1
    Last Post: September 29th 2008, 07:46 AM

Search Tags


/mathhelpforum @mathhelpforum