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Math Help - simultaneous equations

  1. #1
    Newbie
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    Jul 2005
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    21

    solve by addition

    4x-8y=36
    3x-6y=27
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    1,631
    Solve by additon here means do something so that when you add the two equations, one of the variables, the x or the y, is eliminated and you're left with only one variable to find.

    4x -8y = 36 ----(1)
    3x -6y = 27 ----(2)

    We can continue twith those two, if you like, but it will be better if we reduce them to their lowest terms so that we won't be dealing with bigger numbers.

    (1) is divisible by 4, so if we divide both sides by 4,
    x -2y = 9 ---(1a)

    (2) is divisible by 3,
    x -2y = 3 ---(2a)

    Hey, Eqs. (1a) and (2a) are the same!
    Hence, Eqs. (1) and (2) are the same also.
    So there is practically only one equation, with two variables or unknowns.
    That means no unique solutions. Even by addition, by subtraction, by substitution, we cannot solve for x or y.

    Something wrong with your two equations as posted.
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