Results 1 to 3 of 3

Thread: solve the equation

  1. #1
    Junior Member
    Jul 2009

    Post solve the equation

    Hi, can anyone help me solve this


    I multiplyed the first line by -2 and got


    Then added to the second line where I got


    So I got the system :


    Substitute the second line in the first one then solve the system, but still the result aren't that convinsing that it's solved well.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Educated's Avatar
    Aug 2010
    New Zealand
    I personally like the substitution method. It's easy and always works.

    $\displaystyle x^2-y^2=4 \,\,\,\,\, \Longrightarrow \,\,\,\,\, y = \sqrt{x^2 - 4}$

    $\displaystyle 2x^2+2y^2+3x=4$

    Make the substitution of the first equation into the second one.

    $\displaystyle 2x^2+2(\sqrt{x^2 - 4})^2+3x=4$

    $\displaystyle 2x^2+2(x^2 - 4)+3x=4$

    $\displaystyle 4x^2+3x - 12= 0$

    Now that it's in the form of a quadratic, it can easily be solved.

    Your solution works and gives the correct answers as well, however you made it complicated by using both methods of solving simultaneous equations. Stick to one method to keep it simple.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Apr 2005
    I don't know what you mean by "Substitute the second line in the first one then solve the system". You don't substitute "lines" or "equations" you substitute for specific quantities.

    Since there is now no $\displaystyle x^2$ in the first equation, I would solve for $\displaystyle x= -4/3(1+ y^2)$ and substitute that for x in the second equation:
    $\displaystyle (16/9)(1+ 2y^2+ y^4)- y^2= 4$
    $\displaystyle 16+ 32y^2+ 16y^4- 9y^2= 36$
    $\displaystyle 16y^4+ 23y^2- 20 = 0$

    That's now a quadratic equation for $\displaystyle y^2$. One of the two roots will be negative which is impossible since y is real. The positive root will give two roots for y.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Solve Differential equation for the original equation
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: Feb 21st 2011, 01:24 PM
  2. need to solve summation equation to solve sum(x2)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Jul 16th 2010, 10:29 PM
  3. Solve the following equation
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Nov 3rd 2008, 10:20 AM
  4. Replies: 13
    Last Post: May 19th 2008, 08:56 AM
  5. Solve the equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 15th 2008, 07:00 AM

Search Tags

/mathhelpforum @mathhelpforum