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Math Help - An Equation with 4 variable

  1. #1
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    Question An Equation with 4 variable

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

    x = ?

    Thanks Best regards
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  2. #2
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    Re: An Equation with 4 variable

    Hello, blackjack21!

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

    \text{Solve for }x.

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

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

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

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


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

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


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


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

    Then equation [6] says: k = 0.

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

    . . which is true for any value of x.

    I suppose that counts as another solution.
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  3. #3
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    Re: An Equation with 4 variable

    thank you so much for your explanatory answer and Best regards
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