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Math Help - Solving a system of equations?

  1. #1
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    Solving a system of equations?

    http://i52.tinypic.com/2ug14c0.jpg

    Here is a picture of the problem. It gives me a headache haha
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tonydeanxo View Post
    http://i52.tinypic.com/2ug14c0.jpg

    Here is a picture of the problem. It gives me a headache haha
    ln(x^2 + y^2) = 1 + ln(13)

    ln(x + y) = ln(x - y) + ln(8)

    where ln(x) is log to the base e of x. Is this right? Or are they log base 10?

    In either case, what have you been able to do with them?

    -Dan
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  3. #3
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    Have you considered transforming to get rid of the logs? Hint: 10^{log(8)} = 8

    Before transforming, you should worry about Domain issues. Don't lose track of these:

    x + y > 0
    x - y > 0

    Note: I assumed Base 10 logs.
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  4. #4
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    Yes the log bases is 10!
    When i approached the problem. I moved log(13) to the other side and condensed them.
    so it would be log(x^2 +y^2)/13) = 1
    so.. (x^2 +y^2/13) = 10 right?
    so x^2 + y^2 = 130?
    and for the second one
    log(x+y)= log(8(x+y))
    so x+y=8x+8y?
    hmm
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tonydeanxo View Post
    Yes the log bases is 10!
    When i approached the problem. I moved log(13) to the other side and condensed them.
    so it would be log(x^2 +y^2)/13) = 1
    so.. (x^2 +y^2/13) = 10 right?
    so x^2 + y^2 = 130?
    and for the second one
    log(x+y)= log(8(x+y))
    so x+y=8x+8y?
    hmm
    That's correct. Where would you go from there?

    -Dan
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  6. #6
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    Opps on that last comment it is supposed to be 8x-8y
    so then I would solve for an x or y on the second equation.
    so x +y = 8x-8y
    so 7x= 9y
    so either x= 9y/7
    or y= 7x/9
    and plug one of those into the previous equation?
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  7. #7
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    so i get. (9y/7)^2 + y^2 =130
    (81y^2/49) + y^2 = 130
    mulitply all by 49
    81y^2 + y^2 = 6370
    divide by 82. y^2 = 77.68
    y= + or - 8.81?
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tonydeanxo View Post
    so i get. (9y/7)^2 + y^2 =130
    (81y^2/49) + y^2 = 130
    mulitply all by 49
    81y^2 + y^2 = 6370
    81y^2 + 49y^2 = 6730

    You will get y = (+/-) 7. What is x? (Then you have to figure out which +/- signs actually work in the original equation.)

    -Dan
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  9. #9
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    yay. i ended up graphing it and getting 9,7. -9,7 doesn't work thought wuth the logs.
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