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Math Help - Simultaneous equations

  1. #1
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    Simultaneous equations

    x+y=7, x^2 - y^2 = 21
    How do I do this?
    Last edited by Detanon; December 13th 2009 at 09:21 AM. Reason: typo
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  2. #2
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    Quote Originally Posted by Detanon View Post
    x+7=7, xsquared - ysquared = 21
    How do I do this?
    Did you make a typo? I ask because I only see one equation with y in.

    As is stands x =0 and y = \pm i\sqrt{21}
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  3. #3
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    Do you not "see" that x=0 ?
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    woops sorry, I fixed it now.
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  5. #5
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    Quote Originally Posted by Detanon View Post
    woops sorry, I fixed it now.
    As that's better

    You can use the difference of two squares on the quadratic

    (x+y)(x-y) = 7(x-y) = 21 \: \:

    \therefore \: \: x-y = 3  \: \: \rightarrow \: \: x = 3+y

    Sub in x=3+y into the first equation

    (3+y)+y=7

    Solve that for y then use the first equation (in either form) to find x
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  6. #6
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    I dont get how you get (x+y)(x-y).
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  7. #7
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    Quote Originally Posted by Detanon View Post
    I dont get how you get (x+y)(x-y).
    It is the difference of two squares.
    Difference of two squares - Wikipedia, the free encyclopedia

    From the difference of two squares we see that x^2-y^2=(x+y)(x-y)

    If you expand the right hand side using FOIL the LHS is obtained: (x+y)(x-y) = x^2-xy+xy-y^2

    Since -xy+xy=0 we get (x+y)(x-y)=x^2-y^2

    ============================

    EDIT: If you prefer you can use the substitution method

    x = 7-y

    (7-y)^2-y^2=21

    and solve that linear equation (y^2 cancels) but I think using the difference of two squares is easier
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