Results 1 to 5 of 5

Math Help - 6x-y = 21 and 6y - x = 14, x-y?

  1. #1
    Newbie
    Joined
    Feb 2007
    Posts
    16

    6x-y = 21 and 6y - x = 14, x-y?

    As the title says, I want to find x-y, knowing that:

    6x-y = 21 and 6y - x = 14

    I have used substition methods but it seems to be complicating the question which looks as if it should be solved quickly because of its context.

    Any help of how to tackle this problem would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by david18 View Post
    As the title says, I want to find x-y, knowing that:

    6x-y = 21 and 6y - x = 14

    I have used substition methods but it seems to be complicating the question which looks as if it should be solved quickly because of its context.

    Any help of how to tackle this problem would be appreciated.
    subtract the second equation from the first. do you see it?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2007
    Posts
    65
    Try to cancel a variable:

    6x - y = 21
    6y - x = 14

    So I'll try to cancel the x's here:
    6(6y - x) = 6(14)
    36y - 6x = 84

    So now we can cancel the x's to get:

    6x - y = 21 \quad+
    36y - 6x = 84

    35y = 105
    y = 3

    Plug that back into the original equation and:
    6x - 3 = 21
     6x = 24
    x = 4
    Check the values if you want to to make sure they satisfy both equations.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by SnipedYou View Post
    Try to cancel a variable:

    6x - y = 21
    6y - x = 14

    So I'll try to cancel the x's here:
    6(6y - x) = 6(14)
    36y - 6x = 84

    So now we can cancel the x's to get:

    35y = 105
    y = 3

    Plug that back into the original equation and:
    6x - 3 = 21
     6x = 24
    x = 4
    Check the values if you want to to make sure they satisfy both equations.
    this problem was meant to be quick. subtracting the second equation from the first is the fastest way. because you immediately get 7x - 7y = 7 => x - y = 1

    so it's a two liner (and just because we want to be neat, it could be one line if we wish)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    615
    Hello, David!

    Given: . \begin{array}{ccc}6x-y &= & 21 \\ 6y - x &= & 14\end{array}

    \text{Find }\,x-y

    We have: . \begin{array}{ccc}6x-y & = & 21 \\ x - 6y & = & -14\end{array}

    Add the equations: . 7x - 7y \:=\:7

    . . . . . Divide by 7: . \boxed{x - y \:=\:1}


    Darn, too slow again!
    .
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum