business algebra

Use row operations on augmented matrices to solve the given systems of linear equations.

x + y − z = 0
x + 2y + 4z = −3
3x − y − 22z = 19

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  1. 1 1 -1 0
    1 2 4 -3
    3 -1 -22 19

    1 1 -1 0
    0 1 5 -3 --- I did #2 - #1
    0 -4 -19 19 -- I took #3 - 4x#2

    1 1 -1 0
    0 1 5 -3
    0 0 1 7 --- I took #3 - 3x#2

    so z = 7
    in #2: y + 35 = -3
    y = -38

    in #1
    x - 38 - 7 = 0
    x = 45

    x=45 , y=-38 , z=7

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