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Thread: 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.

    $\displaystyle R2: R_2 + R_3$ and $\displaystyle R_1: R1 + 4R_3$


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


    Now do $\displaystyle R_1: R_1 + R_2$


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


    Now you can solve for x. $\displaystyle x = 4$.

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

    $\displaystyle 40 - 5y = 55$

    $\displaystyle -5y = 15$

    $\displaystyle y = -3$.


    $\displaystyle 24 - z = 17$

    $\displaystyle z = 7$.


    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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