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Thread: Elimination (with fractions)

  1. #1
    Junior Member
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    Elimination (with fractions)

    I've thought I had elimination down but adding fractions is making me crazy, help?

    The question that I need help on is.

    m + 3/4n =4
    n - 1/4m = -1
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  2. #2
    MHF Contributor
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    Is the problem

    (1)
    $\displaystyle m + \frac{3}{4}n = 4$

    $\displaystyle n - \frac{1}{4}m = -1$

    or (2)
    $\displaystyle m + \frac{3}{4n} = 4$

    $\displaystyle n - \frac{1}{4m} = -1$

    ?
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  3. #3
    Junior Member
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    It's the first one.

    Forgive me, i'm still new :P
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  4. #4
    MHF Contributor
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    Well, if you don't like fractions, you can get rid of them.

    $\displaystyle m + \frac{3}{4}n = 4$ is equivalent to

    $\displaystyle 4m + 3n = 16$

    and $\displaystyle n - \frac{1}{4}m = -1$ is equivalent to

    $\displaystyle 4n - m = -4$.

    If you can handle fractions, the easiest method comes from adding the two equations $\displaystyle m + \frac{3}{4}n = 4$ and $\displaystyle 4n - m = -4$ to obtain $\displaystyle \left(4 + \frac{3}{4}\right)n = 0$, that is, $\displaystyle n = 0$.
    From this, $\displaystyle m = 4$ quickly follows.
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