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Homework Help: Solve the system.

  1. Sep 14, 2005 #1
    y=x^2
    y=x-1/4

    I really need help with this question. i don't know how to do these types of questions with fractions. i can't think, i need to sleep :zzz:
     
  2. jcsd
  3. Sep 15, 2005 #2

    BobG

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    Edit: I jumped a step. Both equations are equal to y, so [tex]x^2=x-\frac{1}{4}[/tex]

    Get everything onto the same side of the equation. You have a quadratic equation.

    Factoring fractions really isn't that much different than integers. You figure out the combinations that will equal 1/4 when multiplied together. For example:

    [tex]\frac{1}{4}* 1 = \frac{1}{4}[/tex]
    [tex]\frac{1}{2}*\frac{1}{2} = \frac{1}{4}[/tex]

    and so on. Add the combinations together and hopefully one of them will equal your middle coefficient (1 in this case).
     
    Last edited: Sep 15, 2005
  4. Sep 15, 2005 #3

    EnumaElish

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    Then, you can just use the quadratic formula to solve for the roots.
     
  5. Sep 15, 2005 #4

    robphy

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    Note that y=x-1/4 can be rewritten as 4y=4x-1. (No fractions here!)

    As BobG suggests, since y=x^2 replace y in (4y=4x-1) by x^2:
    4(x^2)=4x-1.

    Then, as EnumaElish suggests, use the quadratic formula [after writing it in standard form].


    An alternate method is to plot the two curves (one is a parabola and one is a line) then locate the intersection points.
     
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