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Math Help - set of linear simultaneous equations

  1. #1
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    Algebra Homework Help URGENT!!!

    I have a huge algebra problem, that i need solved for me, and show me how it's done, if possible. Urgent reply needed its due very soon.

    8k - 5n = 8r
    3u + 2o = 189
    5d + 2c = 6m
    5L + 4m = 23b
    3r - m = 3u
    3k - 4i = 2i
    3n - 3o = c
    o - c = 4d
    8i + 9r = 9n
    10m + 7d = 3n
    4d + 4e = 6b
    4y - 6u = 2m
    6b + 3c = 14m

    L + e + n + n + y + c + o + n + u + n + d + r + u + m = ???
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  2. #2
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    Well its sort of a riddle thing, i don't know, but could anyone help?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by drown
    I have a huge algebra problem, that i need solved for me, and show me how it's done, if possible. Urgent reply needed its due very soon.

    8k - 5n = 8r
    3u + 2o = 189
    5d + 2c = 6m
    5L + 4m = 23b
    3r - m = 3u
    3k - 4i = 2i
    3n - 3o = c
    o - c = 4d
    8i + 9r = 9n
    10m + 7d = 3n
    4d + 4e = 6b
    4y - 6u = 2m
    6b + 3c = 14m

    L + e + n + n + y + c + o + n + u + n + d + r + u + m = ???
    This is a set of linear simultaneous equations.

    Reorganise them so that the variables and their coefficients appear on
    the left hand side of each equation, and space them so that the terms
    in a given variable all appear in the same column.

    Then use Gaussian elimination to solve. An explanation of Gaussian elimination
    together with a worked example may be found at:

    http://mathforum.org/library/drmath/view/53207.html

    RonL
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  4. #4
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    Could you show me the answer? It would be a lot easier to figure out if i knew what it was.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by drown
    Could you show me the answer? It would be a lot easier to figure out if i knew what it was.
    Here is DrMath's example:
    Example:

    -4*w + 3*x - 4*y - z = -37
    -2*w - 5*y + 3*z = -20
    -w - x - 3*y - 4*z = -27
    -3*w + 2*x + 4*y - z = 7

    Let w be the first pivot variable, and the first equation the first
    pivot equation. w appears in the second equation, so we subtract
    (-2)/(-4) = 1/2 times the first equation from the second, getting

    -2*w - 5*y + 3*z = -20,
    -2*w + (3/2)*x - 2*y - (1/2)*z = -37/2
    --------------------------------------
    -(3/2)*x - 3*y + (7/2)*z = -3/2

    w appears in the third equation so we subtract (-1)/(-4) times the
    first equation from the third. w appears in the fourth equation, so we
    subtract (-3)/(-4) times the first equation from the fourth. This
    leaves

    -4*w + 3*x - 4*y - z = -37
    -(3/2)*x - 3*y + (7/2)*z = -3/2
    -(7/4)*x - 2*y - (15/4)*z = -71/4
    -(1/4)*x + 7*y - (1/4)*z = 139/4

    Now the last three equations are a system of three equations in three
    unknowns, and we treat that similarly. Let x be the next pivot
    variable, and the second equation the pivot equation. Since x appears
    in the third equation, we subtract (-7/4)/(-3/2) = 7/6 times the
    second equation from the third. Since x appears in the fourth equation
    we subtract (-1/4)/(-3/2) = 1/6 times the second equation from the
    fourth. This leaves

    -4*w + 3*x - 4*y - z = -37
    -(3/2)*x - 3*y + (7/2)*z = -3/2
    (3/2)*y - (47/6)*z = -16
    (15/2)*y - 16*z = 35

    Now the last two equations are a system of two equations in two
    unknowns, and we treat that similarly. Let y be the next pivot
    variable, and the third equation the next pivot equation. Since y
    appears in the fourth equation, we subtract (15/2)/(3/2) = 5 times the
    third equation from the fourth. This leaves

    -4*w + 3*x - 4*y - z = -37
    -(3/2)*x - 3*y + (7/2)*z = -3/2
    (3/2)*y - (47/6)*z = -16
    (115/3)*z = 115

    This completes the first phase.

    Now we start with the last equation, and solve for z. This gives
    z = 3, and we substitute that into the preceding equations:

    -4*w + 3*x - 4*y = -34
    -(3/2)*x - 3*y = -12
    (3/2)*y = 15/2

    The last remaining equation tells us that y = 5, and we substitute
    that into the preceding equations:

    -4*w + 3*x = -14
    -(3/2)*x = 3

    The last remaining equation tells us that x = -2, and we substitute
    that into the preceding equation:

    -4*w = -8

    That gives us the value w = 2, and so the solution is

    (w,x,y,z) = (2,-2,5,3)

    Understood?
    and the answer in this case is:

    b=20, c=30, d=6, e=24, i=36, k=72, l=80, m=15, n=64, o=54, r=32, u=27, y=48.

    I will not reproduce the actual manipulations here as they are a bit
    long and would be too much typing.

    RonL
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