Results 1 to 4 of 4

Math Help - Simultaneous Equations

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Simultaneous Equations

    x(x+y+z)=2-yz
    y(x+y+z)=4-xz
    z(x+y+z)=8-yx

    Find the value of |x+y+z|

    I know \sqrt{(x+y+z)^2}=|x+y+z|

    But I'm stuck on (x+y+z)^2=14-(xy+yz+xz)

    Any tips?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576

    Re: Simultaneous Equations

    It might help if you realise from your equations that \displaystyle x + y + z = \frac{2 - yz}{x} = \frac{4 - xz}{y} = \frac{8 - yx}{z}.

    See what you can do with the latter three equations.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Re: Simultaneous Equations

    Have tried cross multiplying them, nothing works out right now.
    Any other options?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,240
    Thanks
    1795

    Re: Simultaneous Equations

    x(x+ y+ z)= 2- yz
    y(x+ y+ z)= 4- xz
    x(x+ y+ z)= 8- yz



    Find the value of |x+ y+ z|

    I know \sqrt{(x+ y+ z)^2}= |x+ y+ z|

    But I'm stuck on (x+ y+ z)^2= 14- (xy+ xz+ yz)

    Any tips?
    Well, why not just take the square root of both sides?
    |x+ y+ z|= \sqrt{14- (xy+ xz+ yz)}
    Last edited by HallsofIvy; August 29th 2011 at 05:20 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simultaneous Equations 4 variables, 4 equations
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 7th 2011, 05:06 PM
  2. Simultaneous Equations.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 13th 2011, 01:57 PM
  3. Replies: 3
    Last Post: February 27th 2009, 08:05 PM
  4. Simultaneous Equations
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 21st 2008, 05:29 PM
  5. Simultaneous equations?
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: June 24th 2008, 07:32 AM

Search Tags


/mathhelpforum @mathhelpforum