1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Solve the system.

  1. Sep 14, 2005 #1

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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:

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook