Results 1 to 3 of 3

Thread: An Equation with 4 variable

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Newyork
    Posts
    14

    Question An Equation with 4 variable

    2y+3k=5u
    2u+4y=3k
    3k=ux

    x = ?

    Thanks Best regards
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848

    Re: An Equation with 4 variable

    Hello, blackjack21!

    $\displaystyle \begin{array}{cc}2y+3k\:=\:5u & [1] \\ 2u+4y\:=\:3k & [2] \\ ux\:=\:3k & [3] \end{array}$

    $\displaystyle \text{Solve for }x.$

    From [1]: .$\displaystyle y \:=\:\frac{5u-3k}{2}\;\;[4]$

    From [2]: .$\displaystyle y \:=\:\frac{3k-2u}{4}\;\;[5]$

    Equate [4] and [5]: .$\displaystyle \frac{5u-3k}{2} \:=\:\frac{3k-2u}{4} \quad\Rightarrow\quad 20y - 12k \:=\:6k-4u$

    . . . $\displaystyle 24u \:=\:18k \quad\Rightarrow\quad k \:=\:\tfrac{4}{3}u\;\;[6]$


    Substitute into [3]: .$\displaystyle ux \:=\:3\left(\tfrac{4}{3}u\right) \quad\Rightarrow\quad ux \:=\:4u $

    Divide by $\displaystyle u\!:\;\;x \:=\:4$


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    After dividing by $\displaystyle u$, I had to consider: what if $\displaystyle u = 0\,?$

    Then equation [6] says: $\displaystyle k = 0.$

    And equation [3] becomes: .$\displaystyle 0\cdot x \:=\:3\cdot0 \quad\Rightarrow\quad 0 \:=\:0$

    . . which is true for any value of $\displaystyle x.$

    I suppose that counts as another solution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Newyork
    Posts
    14

    Re: An Equation with 4 variable

    thank you so much for your explanatory answer and Best regards
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Aug 3rd 2010, 08:08 PM
  2. 3 variable equation? Please help!!!
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Jun 9th 2010, 10:52 AM
  3. four variable equation
    Posted in the Algebra Forum
    Replies: 6
    Last Post: Dec 22nd 2009, 06:15 AM
  4. Variable Equation help
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Dec 11th 2009, 08:16 AM
  5. Three variable equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Feb 19th 2009, 07:00 PM

Search Tags


/mathhelpforum @mathhelpforum