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Math Help - Having trouble solving for a couple of variables

  1. #1
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    Having trouble solving for a couple of variables

    It has been a while since I've had a math class and was having trouble solving for two variables. Here are the two equations I have:

    a+b=w+x+y+z
    ab=wy+wx+xz

    I am trying to solve for a and b individually but am really having trouble. Am I missing something?
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  2. #2
    Senior Member sakonpure6's Avatar
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    Re: Having trouble solving for a couple of variables

    I was trying to solve this but hit a wall when I pluged equation 1 into 2. Here is what I did, maybe it will help you just a bit.

    Spoiler:
    If we are solving for a and b, then they will be represented in terms of everything else. In this case w,x,y,z.

    From equation 1:
    a+b=w+x+y+z \newline a=w+x+y+z-b or b=w+x+y+z-a
    In any case just take the determined value of a or b from above and plug it into the second equation and isolate for the desired variable.
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    Re: Having trouble solving for a couple of variables

    I also tried that and that's where I got stuck.
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    Forum Admin topsquark's Avatar
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    Re: Having trouble solving for a couple of variables

    Quote Originally Posted by thealbatross View Post
    It has been a while since I've had a math class and was having trouble solving for two variables. Here are the two equations I have:

    a+b=w+x+y+z
    ab=wy+wx+xz

    I am trying to solve for a and b individually but am really having trouble. Am I missing something?
    b = w + x + y + z - a means that a(w + x + y + z - a) = wx + wy + xz. Expanding it out gives

    -a^2 + (w + x + y + z)a = wx + wy + xz

    a^2 - (w + x + y + z)a + (wx + wy + xz) = 0

    This is a quadratic equation in a and you can use the quadratic formula. It's going to be a terrible mess as I doubt it is going to give you any sort of "simple" answer.

    -Dan
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