Algebra 2

Solving Systems of Equations in Three Variables:

3x+3y-z=-3
-2x-3y+2z=3
x-6y+3z=0

PLease show work

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  1. +3x + 3y - z = -3
    -2x - 3y + 2z = 3
    x - 6y + 3z = 0

    Eq1: 3x + 3y - z = -3
    Eq2: -2x - 3y + 2z = 3
    Sum: x + 0 + z = 0
    z = -x

    Eq2: -2x - 3y + 2z = 3
    Eq3: x - 6y + 3z = 0
    Multiply Eq2 by 6 and Eq3 by (-3):
    -12x - 18y + 12z = 18
    -3x + 18y - 9z = 0
    Sum: -15x + 0 + 3z = 18
    Replace z with -x:
    -15x-3x = 18
    -18x = 18
    X = -1

    Z = -x = 1.

    In Eq1, replace X with -1. and z with 1:
    3*(-1) + 3y - 1 = -3
    -3 + 3y -1 = -3
    3y = 1
    Y = 1/3

    Solution = (X, Y, Z) = (-1, 1/3, 1).

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