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29 April, 10:30

Which classification best describes the following system of equations? 3x+6y-12z=36, x+2y-4z=12, 4x+8-16z=48

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  1. 29 April, 10:36
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    (1) 3x+6y-12z=36

    (2) x+2y-4z=12

    (3) 4x+8y-16z=48

    The first equation (1) is the second equation (2) multiplied by 3:

    (2) x+2y-4z=12→3 (x+2y-4z=12) →3x+6y-12z=36 (1)

    The third equation (3) is the second equation (2) multiplied by 4:

    (2) x+2y-4z=12→4 (x+2y-4z=12) →4x+8y-16z=48 (3)

    The equations are linearly dependent, Then the system of equations is dependent, and then consistent too.
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