Results 1 to 4 of 4

Math Help - Sysyem

  1. #1
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    541

    Sysyem

    Solve the system in R :
    x + y = 1
    y + z = 1
    x + z = 1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    31
    Guideline

    express y as function of x
    put it in second equation
    express z as function of x
    put in third equation
    find z
    put z in second equation
    find y
    put y in first equation
    find x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,908
    Thanks
    767
    Hello, dhiab!

    Solve the system in R:

    . . \begin{array}{cccccccc}<br />
x & + & y & & & = & 1 & [1] \\<br />
& & y & + & z & = & 1 & [2] \\<br />
x & & & + &z & = & 1 & [3] \end{array}

    \begin{array}{ccccc}\text{Subtract [1]-[2]:} & x - z &=& 0 \\<br />
\text{Add [3]:} & x + z &=& 1 \end{array}

    And we have: . 2x \:=\:1 \quad\Rightarrow\quad \boxed{x \:=\:\tfrac{1}{2}}

    Substitute into [1]: . \tfrac{1}{2} + y \:=\:1 \quad\Rightarrow\quad\boxed{ y \:=\:\tfrac{1}{2}}

    Substitute into [2]: . \tfrac{1}{2} + z \:=\:1 \quad\Rightarrow\quad \boxed{z \:=\:\tfrac{1}{2}}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Another approach:

    Add all the equations: 2(x+y+z)=3\Rightarrow x+y+z=\frac{3}{2}.

    x+y=1\Rightarrow z=\frac{1}{2}

    y+z=1\Rightarrow x=\frac{1}{2}

    x+z=1\Rightarrow y=\frac{1}{2}
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum