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Math Help - solving systems of equations

  1. #1
    Junior Member wpcp15's Avatar
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    Question solving systems of equations

    r + s + t=5
    2r + 7s - 3t=13
    1/2r - 1/3s + 2/3t=-1

    I get confused when I come to the fractions.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wpcp15 View Post
    r + s + t=5
    2r + 7s - 3t=13
    1/2r - 1/3s + 2/3t=-1

    I get confused when I come to the fractions.
    So get rid of them. Multiply the bottom equation by 6. The bottom equation becomes:
    3r - 2s + 4t = -6

    and solve the system of equations with this.

    -Dan
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  3. #3
    Junior Member wpcp15's Avatar
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    Thank You
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  4. #4
    Junior Member wpcp15's Avatar
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    1 more question

    One more question, what about?

    a + b=3
    -b + c=3
    a +2c=10
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  5. #5
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    Quote Originally Posted by wpcp15 View Post
    One more question, what about?

    a + b=3
    -b + c=3
    a +2c=10
    Add the first two,
    a+c=6
    a+2c=10
    From third subtract this result,
    c=4
    Thus,
    a=2
    Thus,
    b=1
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  6. #6
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    a + b = 3
    -b + c = 3
    a + 2c = 10

    It's so easy after making it into a matrix:

    1 1 0 3
    0 -1 1 3
    1 0 2 10

    Where the last column is the augmented matrix (the = part).

    Row reduce the rows:

    1 0 0 2
    0 1 0 1
    0 0 1 4

    x_1 = 2
    x_2 = 1
    x_3 = 4

    x_1, x_2, x_3 -> a, b, c, respectively.

    Try it with the first equation.
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