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System of equations with 2 parameters

  1. Jun 2, 2013 #1
    1. The problem statement, all variables and given/known data
    I have a system of two equations:

    3*x^2 - x + 3*y^2 = 0
    2*x^2 - y + 2*y^2 = 0

    2. Relevant equations



    3. The attempt at a solution
    I don't know how to express one with the other.I mean I can either have x = 3*y^2 + 3*x^2 or y = y = -2*y^2 - 2*x^2 and in both cases it becomes an utter mess.What can I do?
     
  2. jcsd
  3. Jun 2, 2013 #2

    mfb

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    I would modify the second equation to get x^2 = ... and therefore x = ... and use this in the first equation.
     
  4. Jun 2, 2013 #3

    LCKurtz

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    Here's another suggestion. You can see by inspection that (0,0) is one intersection point. Since both equations represent circles, put them in standard form and locate their centers. Determine the slope ##m_1## of the line of centers. The slope of the common chord between their intersection points will be ##m_2=-\frac 1 {m_1}##. The line through the origin with that slope ##m_2## whose equation is ##y=m_2x## will pass through the other intersection point. Solve that with one of your circles. It works out pretty easily.
     
  5. Jun 3, 2013 #4

    haruspex

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    One more suggestion: can you spot a multiplier that makes the quadratic terms in one equation the same as those in the other?
     
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