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Math Help - Gaussian Elimination

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    Exclamation Gaussian Elimination

    The problem is:

    2x + 5y + 4z = 21
    4x - 5y +z = 38
    6x - z = 17

    step by step please.
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  2. #2
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    Quote Originally Posted by helpme View Post
    The problem is:

    2x + 5y + 4z = 21
    4x - 5y +z = 38
    6x - z = 17

    step by step please.
    Usually I would say to eliminate the x values first, but in this case it looks easier to eliminate the z's.

    Do the following.

    R2: R_2 + R_3 and R_1: R1 + 4R_3


    26x + 5y = 87
    10x - 5y = 55
    6x - z = 17


    Now do R_1: R_1 + R_2


    36x = 144
    10x - 5y = 55
    6x - z = 17.


    Now you can solve for x. x = 4.

    Substitute this value into the other two equations to solve for y and z.

    40 - 5y = 55

    -5y = 15

    y = -3.


    24 - z = 17

    z = 7.


    So your solution is [tex](x, y, z) = (4, -3, 7).

    You could substitute these back into your original equation to check if you wish.
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