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Math Help - simple simultaneous equations?

  1. #1
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    simple simultaneous equations?

    Hello, can someone help me sovle these, i know the gaussian and substitution methods but the coefficients in these equations are all proportional so when i multiply up to cancel out it removes all Xs and all Ys, any suggestions are welcome, it's probably really simple and i'm missing something, thanks guys.

    10x+2y=8 and;
    3y+15x=12

    thanks again .
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  2. #2
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    Quote Originally Posted by captainlewis View Post
    Hello, can someone help me sovle these, i know the gaussian and substitution methods but the coefficients in these equations are all proportional so when i multiply up to cancel out it removes all Xs and all Ys, any suggestions are welcome, it's probably really simple and i'm missing something, thanks guys.

    10x+2y=8 and;
    3y+15x=12

    thanks again .
    10x+2y=8...(1)
    15x+3y=12...(2)

    Equation (1) and (2) are really the same. To see this multiply (1) by 15.

    Work with equation (1).

    10x+2y=8
    Thus,
    5x+y=4
    Thus,
    y=-5x+4

    Let x=t i.e. and real number.
    Then, y=-5x+4=-5t+4

    Thus,
    x=t
    y=-5t+4

    Are all solutions.
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  3. #3
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    Hello, captainlewis!

    You're not missing a thing.
    . . The system does not have a unique solution.


    10x + 2y .= .8 . [1]
    15x + 3y .= 12 -[2]

    Divide [1] by 2: .5x + y .= .4
    Divide [2] by 3: .5x + y .= .4

    You see, they gave us only one equation.

    And one equation with two variables has an infinite number of solutions.

    It says: "Find two numbers x and y so that 5 times x plus y equals 4"
    . . and there are zillions of answers: .(1,-1), (0,4), (-1,9), . . .

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