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Math Help - Simultaneous Equations 4 variables, 4 equations

  1. #1
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    Simultaneous Equations 4 variables, 4 equations

    Hi,

    I have 4 simultaneous equations with 4 variables. I thought that was enough to be able to solve it but I can't figure it out (or else, why it can't be figured out)


    a + b = 4903716584 (1)
    c + d = 4316123816 (2)
    c + a = 3628610024 (3)
    d + b = 5591230376 (4)

    From these I went this way

    (1)-(3) b - c = 4903716584 - 3628610024 = 1275106560
    (1)-(4) a - d = 4903716584 - 5591230376 = -687513792
    (2)-(3) gives -((1)-(4))
    (2)-(4) gives -((1)-(3))

    that doesn't seem a lot of help. I am not able to isolate any single variable.
    Can someone help please ?

    thx
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  2. #2
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    Re: Simultaneous Equations 4 variables, 4 equations

    Quote Originally Posted by MathFan View Post
    Hi,

    I have 4 simultaneous equations with 4 variables. I thought that was enough to be able to solve it but I can't figure it out (or else, why it can't be figured out)


    a + b = 4903716584 (1)
    c + d = 4316123816 (2)
    c + a = 3628610024 (3)
    d + b = 5591230376 (4)

    From these I went this way

    (1)-(3) b - c = 4903716584 - 3628610024 = 1275106560
    (1)-(4) a - d = 4903716584 - 5591230376 = -687513792
    (2)-(3) gives -((1)-(4))
    (2)-(4) gives -((1)-(3))

    that doesn't seem a lot of help. I am not able to isolate any single variable.
    Can someone help please ?

    thx
    Unfortunately for you, the four equations are not independent: determinant of {{1, 1, 0, 0}, {0, 0, 1, 1}, {1, 0, 1, 0}, {0, 1, 0, 1}} - Wolfram|Alpha

    This means that you don't really have 4 equations with 4 unknowns. Some of the equations can be obtained from the others and so are therefore redundant. Your system does not have a unique solution.

    eg.
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  3. #3
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    Re: Simultaneous Equations 4 variables, 4 equations

    Thx for the very quick reply. That's just what I was thinking. However, I've just noticed I missed one equation that might make the difference

    a+d = b+c

    I'll have another look at it now
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  4. #4
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    Re: Simultaneous Equations 4 variables, 4 equations

    Yes, that leaves it solvable, thx for your help mr fantastic.
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