Math-System of Equations

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1. Solve for x, y, z in the following system:

2x-3y-2=z
y-x+z=1
-y-2z=7

The answers are: x=-7 y=-5 and z=-1 however I don't know how to go about this.

  • Math-System of Equations -

    From the 3rd: y = -2z-7

    in the 1st:
    2x - 3(-2z-7) - z = 2
    2x +6z +21 - z = 2
    2x + 5z = -19 (#4)

    in the 2nd:
    -2z - 7 - x + z = 1
    x + z = -8
    2x + 2z = -16 (#5)

    #4 - #5 :
    3z = -3
    z = -1
    sub into y = -2z-7 ---> 2-7 = -5
    sub into 2nd:
    -5 - x - 1 = 1
    -x = 7
    x = -7

    so , x = -7, y = -5 and z = -1

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