Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By kalyanram

Math Help - Find all solutions

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    Find all solutions

    Find all solutions to this system of equations
    3x^2y-3y=0 (i)
    x^2-3x-2y=0 (ii)


    I take
    3(ii) 2(i) = 0


    => 6x^2y-6y=3x^3-9x (2)
    => 6y(x^2-1)=3x(x^2-3) (3)

    Therefor, I have these points.
    (0,0)
    (√3, 0)

    But x=1 is also a solution. But that doesn't satisfy the right hand side in (3). I could have seen x=1 and put it in (i) and (ii). But I didn't see that. Do I have a bad, nonsystematic method for solving this system of equation? How do I do it better?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member kalyanram's Avatar
    Joined
    Jun 2008
    From
    Bangalore, India
    Posts
    143
    Thanks
    14

    Re: Find all solutions

    Equation (2) is incorrect. As you have a x^3 term which is not present in the original equation.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member kalyanram's Avatar
    Joined
    Jun 2008
    From
    Bangalore, India
    Posts
    143
    Thanks
    14

    Re: Find all solutions

    Quote Originally Posted by jacob93 View Post
    But x=1 is also a solution. But that doesn't satisfy the right hand side in (3). I could have seen x=1 and put it in (i) and (ii). But I didn't see that. Do I have a bad, nonsystematic method for solving this system of equation? How do I do it better?
     3x^2y-3y=0 - (1), x^2-3x-2y=0 - (2)
    From Eq (1) we have
     3y(x-1)(x+1)=0 satisfied by y=0, x= \pm 1
    When y=0 have x=0,3 from Eq(2)
    When x=1 have y=-1 from Eq(2)
    When x=-1 have y=1 from Eq(2)

    So solutions are (0,0), (0,3), (1,-1), (-1,1)
    Thanks from jacob93
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    Re: Find all solutions

    Quote Originally Posted by kalyanram View Post
    When x=1 have y=-1 from Eq(2)
    How? When x=1, then 6y-6y=3-9 which never happens.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member kalyanram's Avatar
    Joined
    Jun 2008
    From
    Bangalore, India
    Posts
    143
    Thanks
    14

    Re: Find all solutions

    Quote Originally Posted by jacob93 View Post
    How? When x=1, then 6y-6y=3-9 which never happens.
    As I have already indicated in my previous post the equation you have referred to as Eq(2) is incorrect as it should have eliminated the y term and should not have a x^3 term.

    The Eq(2) I have mentioned is the second of the original two equations.
    Last edited by kalyanram; September 14th 2012 at 09:28 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    Re: Find all solutions

    thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find solutions of z bar = z^2
    Posted in the Pre-Calculus Forum
    Replies: 19
    Last Post: August 29th 2011, 02:50 AM
  2. Find all solutions
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 17th 2010, 11:49 AM
  3. Find all solutions
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 10th 2010, 08:34 AM
  4. Find all solutions in Z16...
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 28th 2009, 12:43 PM
  5. find all solutions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 23rd 2009, 04:26 PM

Search Tags


/mathhelpforum @mathhelpforum