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multi-variable equations

  1. #1
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    multi-variable equations

    Does anyone have any experience or know of a way to solve multi-variable equations using Excel. For instance, I have the following three-equation system and would like to solve for X, Y and Z.

    X+Y-5-Z=25
    5Z-Y/2+X=-14
    Y+2X+5Z=88

    The solution to something as simple as this is pretty straighforward, however, I have some much more complicated 3-equation systems I would lke to solve.

  2. #2
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    Use the matrix/determinant function MDETERM() to solve simultaneous equations:
    1. You must write the equations in STANDARD FORM, i.e.,
    X1+ Y1 + Z1 = C1
    X2+ Y2 + Z2 = C2
    X3+ Y3 + Z3 = C3
    Put each numeric value in a cell, for your example, using cells A1:D3 the matrix is:
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    Copy/paste cells A1:C3 three times, these will be your X, Y & Z determinants.
    Next, copy cells D1:D3
    Paste these D values over the:
    X column of the X determinant,
    Y col of the Y det'mt, &
    Z col of the Z det'mt, thus:
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    Use the function: MDETERM() to calculate four determinants:
    The first determinant using =MDETERM(A1:C3) is the determinant D of the matrix and will be the divisor.

    Use the MDETERM fn on each of the remaining three arrays and divide the results of each by D

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    Therefore:
    X = 255/-4.5 = -56.67
    Y = -476/-4.5 = 105.78
    Z= -86/-4.5 = 19.11
    Ben Van Johnson

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