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Simultaneous equation question

  1. Oct 30, 2005 #1
    Hey just need my answer to be checked on this problem
    just to clarify x2 means x squared!

    Solve the following

    y = 2 - x
    x2 + 2xy = 3

    Substitute equations

    x2 + 2x(2 - x) = 3
    x2 + 4x - 2 x2 = 3
    -x2 + 4x - 3 = 0

    Factorising

    (-x + 1) (x - 3) = 0

    so x = -1 and 3
    _____________________________________________

    as y = 2 - x

    y = 2 - 3
    = -1

    y = 2 + 1
    = 3

    so the co ordinates for the two roots of this curve will be

    (-1, 3) and (3, -1)

    is this the right answer? i believe it to be, but my answer books says differently!

    Please check my answer.
    Thanx in advance!
     
  2. jcsd
  3. Oct 31, 2005 #2
    You made a small mistake where I highlighted.
     
  4. Oct 31, 2005 #3
    sorry, i still don't understand, i checked what i did, i can't see whats wrong with the bit highlighted!

    Can anyone elaborate?
     
  5. Oct 31, 2005 #4

    TD

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    Homework Helper

    I didn't read it all but if your factorization was correct, then x = 1 is a solution and not x = -1.
     
  6. Oct 31, 2005 #5
    i think i see what i have done wrong

    the x = 3 is right

    but it is -x = -1!

    so x = 1

    so to start again............

    as y = 2 - x
    y = 2 - 3
    = -1
    y = 2 - 1
    = 1
    so the co ordinates for the two roots of this curve is
    (-1, 3) and (1, 1)

    Thanx a lot, this is the answer in the book, easy mistake i made i think! bah humbug with the positive and negative signs!!

    Cheers! I can sleep now!
     
  7. Oct 31, 2005 #6

    TD

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    Good :smile:
     
  8. Nov 1, 2005 #7

    verty

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    A word of advice, when you factorise like that it usually helps to have the x^2 coefficient be positive.
     
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