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Math Help - Help solving equations please

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    40

    Cool Help solving equations please

    I am working through an old book and an example has these two equations that need to be used to solve for x and y:
    xm + y = m
    x + yn = n

    The solution has x = (mn - n) / (mn - 1 ) and y = (mn - m) / (mn - 1).
    I keep getting the wrong answer!

    Please help show me the way to the answer.
    Thanks,
    Ultros
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Hello, Ultros88!

    There are several ways to solve this system.
    I'll use "Elimination" . . .


    \begin{array}{cccc}mx + y &=&  m & {\color{blue}[1]}\\ x + ny &= &n & {\color{blue}[2]}\end{array}

    The solution is: . \begin{array}{ccc} x& =&\dfrac{mn - n}{mn - 1} \\ \\[-3mm] y &= &\dfrac{mn - m}{mn - 1} \end{array}

    \begin{array}{cccccc}\text{Multiply {color{blue}[1]} by }n\!: & mnx &+& ny &=& mn \\ \text{Subtract {\color{blue}[2]}:} & x &+& ny &=& n \end{array}

    And we have: . mnx - x \;=\;mn - n \quad\Rightarrow\quad x(mn-1) \;=\;mn - n

    . . Therefore: . \boxed{x \;=\;\frac{mn-n}{mn-1}}


    \begin{array}{cccccc}\text{Multiply {color{blue}[2]} by }m\!: & mx &+& mny &=& mn \\ \text{Subtract {\color{blue}[1]}:} & mx &+& y &=& m \end{array}

    And we have: . mny - y \:=\:mn - m \quad\Rightarrow\quad y(mn-1) \:=\:mn-m

    . . Therefore: . \boxed{ y \;=\;\frac{mn-m}{mn-1}}

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