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System of equations : Help

  1. Sep 14, 2009 #1
    I have been trying to solve this problem for a whole week without success, I need help.

    Solve the following for x,y and z:

    2x+5y-z = 18
    7x-y+4z = 22
    6x+2y-3z = 0.1x + 0.2y + 0.3z

    I have already combined all the terms of eq.#3 and equal it to zero, but it didn't work.
    I also, multiplyed eq.#3 by 1 and tried to have a comon x for the other two equations to eliminate x and it didn't work, I've tried many other tatics but it doesn't work.

    please help
    Thank you
     
  2. jcsd
  3. Sep 15, 2009 #2

    CRGreathouse

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    Pari:
    Code (Text):
    matsolve([2,5,-1;7,-1,4;6-.1,2-.2,-3-.3],[18,22,0]~)
    TI-BASIC:
    Code (Text):
    rref([[2,5,-1,18][7,-1,4,22][6-.1,2-.2,-3-.3,0]])
    Matlab:
    Code (Text):
    linsolve([2 5 -1; 7 -1 4; 6-.1 2-.2 -3-.3], [18; 22; 0])
    Mathematica:
    Code (Text):
    LinearSolve[{{2,5,-1}{7,-1,4}{6-.1,2-.2,-3-.3}},{18,22,0}]
     
  4. Sep 15, 2009 #3
    Maybe you can show some steps or explain in more detail what your problem is? Show us where you're getting stuck or explain what "it didn't work" means.

    -Kerry
     
  5. Sep 15, 2009 #4

    HallsofIvy

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    2x+ 5y- z= 18
    7x- y+ 4z= 22
    5.9x+ 1.8y- 3.3z= 0 ?

    Why in the world would you multiply anything by "1"? Do you mean "10"? That would give you 59x+ 18y- 33z= 0. Getting a "common x" for the other two equations (I guess you mean the same coefficient) would give 14x+ 35y- 7z= 119 and 14x- 5y+ 20z= 110. Subtracting the second equation from the first gives 40y- 27z= 9. What do you mean "it doesn't work"?

    The equations above are the
     
  6. Sep 15, 2009 #5
    Ahhh - I read it the same way HallsOfIvy did the first time - perhaps you multiplied eq. 3 by eq. 1? Maybe this is the problem - you don't want to multiply, you want to add. Really, you should multiply an equation by a carefully selected constant, then add it to another equation. For example, if you multiply eq. 1 by 4, and add it to eq. 2, you get

    [tex]8x + 20y - 4z + 7x - y +4z = 72 + 22[/tex]
    or
    [tex]15x + 19y = 94[/tex]

    Does this help get you started?

    -Kerry
     
    Last edited: Sep 15, 2009
  7. Sep 16, 2009 #6

    hotvette

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    Homework Helper

  8. Sep 17, 2009 #7
    Thank you everyone,
    I was confused, but with your help found the solution to this problem
     
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