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Math Help - algebra help

  1. #1
    fly
    Guest

    Angry Stuck

    Solve for m and n:
    2m-n=3

    mē - mn+nē =3
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Here is one way, by substitution.

    2m -n = 3 ------(1)

    mē -mn +nē = 3 ---------(2)

    From (1),
    2m -3 = n, or, n = 2m -3
    Substitute that into (2)
    m^2 -m(2m -3) +(2m -3)^2 = 3
    m^2 -(2m^2 -3m) +(4m^2 -12m +9) = 3
    m^2 -2m^2 +3m +4m^2 -12m +9 -3 = 0
    Collect like terms,
    (m^2 -2m^2 +4m^2) +(3m -12m) +(9 -3) = 0
    3m^2 -9m +6 = 0
    Get its simplest form, divide both sides by 3,
    m^2 -3m +2 = 0
    Factor that,
    (m -2)(m-1) = 0

    m-2 = 0
    So, m= 2

    m -1 = 0
    So, m = 1

    When m=2,
    n = 2m -3 = 2*2 -3 = 1

    When m=1,
    n = 2m -3 = 2*1 -3 = -1

    Therefore, there are two sets of answer:
    m=2, n=1 ----------answer.
    m = 1, n = -1 ----------answer.
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