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Math Help - Linear system of equations. 3 equations, 3 variables

  1. #1
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    Linear system of equations. 3 equations, 3 variables

    I understand how to solve it, but there is just something that I don't understand:

    3a + b + 2c = 21 + 1/2
    8a + 3b + 5c = 57
    a + b + c = 10

    What I don't understan is why I can do this:

    8a + 3b + 5c = 57
    +
    a + b + c = 10
    =
    9a + 4b + 6c = 67

    and then:

    3a + b + 2c = 21 + 1/2 *(-3)
    -9a - 3b - 6c = -63 - 3/2

    9a + 4b + 6c = 67
    -9a - 3b - 6c = -63 - 3/2

    and the rest is substitution.
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  2. #2
    Junior Member piglet's Avatar
    Joined
    Feb 2010
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    well you're not changing any of the values of a,b or c by performing operations like multiplying one of the equations by a number or by adding two equations together to get a sum.

    I'm sure someone with a better way of words (and perhaps a bit more knowledge) will explain it better..
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  3. #3
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    I did a quick search and found that multiplying and adding up equations come from "gauss elimination", which in turn, is related to matrices.
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