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Math Help - Use the echelon method to solve the following system of two equations in two unknowns

  1. #1
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    Use the echelon method to solve the following system of two equations in two unknowns

    x+y=6
    4x-y=19

    Thank you
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  2. #2
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    Re: Use the echelon method to solve the following system of two equations in two unkn

    Quote Originally Posted by Niaboc View Post
    x+y=6
    4x-y=19

    Thank you
    You need to put it in matrix form, then row reduce.

    So, start with:
    [1 1 6
    4 -1 19]

    Add row 1 to row 2:
    [1 1 6
    5 0 15]

    Divide row 2 by 5:
    [1 1 6
    1 0 3]

    Swap rows:
    [1 0 5
    1 1 6]

    At this point, you have echelon form. The easiest way to go from here is to note x = 5, and substitute into y + x = 6.
    However, if you need to be in reduced echelon form:
    Subtract row 1 from row 2:
    [1 0 5
    0 1 1]

    This gives you the two solution equations:
    x = 5
    y = 1

    Hope this helps.
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