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Nonlinear Systems

  1. Jun 5, 2009 #1
    1. The problem statement, all variables and given/known data
    solve the system of [tex]3x^{2}+2y^{2}=35[/tex] and
    [tex]4x^{2}-3y^{2}=24[/tex]


    2. Relevant equations



    3. The attempt at a solution
    I re arranged for y^2 and got [tex]1\frac{1}{3}x^{2}-16=y^{2}[/tex] I keep getting x to equal \pm 2.473 this is clearly wrong, the answers should be (–3, –2), (–3, 2), (3, –2), and (3, 2). What am I doing wrong?
     
  2. jcsd
  3. Jun 5, 2009 #2

    rock.freak667

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    Homework Helper

    Instead of messing with fractions, why not just multiply the first equation by 3, the second equation by 2 and then just add them?
     
  4. Jun 5, 2009 #3
    Thanks for the help but I still have a question, after I combined the two equations how come it worked and it didn’t work when I rearranged them. Did I mess up?
     
  5. Jun 5, 2009 #4

    HallsofIvy

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    Looks like a basic arithmetic error. Because of the "[itex]1\frac{1}{3}[/itex]", which would better be left 4/3, it looks like you solved the second equation for y2: [itex]3y^2= 4x^2- 24[/itex] so [itex]y^2= (4/3)x^2- 8[/itex]. 24/3= 8, not 16.
     
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