Algebra

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I need help I don't know how to solve this system

Solve the following system. Show all your work

3x-2y+2z= 30
-x+3y-4z= -33
2x-4y+3z= 42

  • Algebra -

    Eq1: 3x-2y+2z = 30
    Eq2: -x+3y-4z = -33
    Eq3: 2x-4y+3z = 42

    Multiply Eq1 by 2 and add Eq1 and Eq2:
    6x-4y+4z = 60
    -x+3y-4z = -33
    Eq4:5x-y = 27 = Sum.

    Multiply Eq2 by 3 and Eq3 by 4 and add Eq2 and Eq3:
    -3x+9y-12z = -99
    8x-16y+12z = 168
    Eq5: 5x-7y = 69

    Multiply Eq4 by -1 and add Eq4 and Eq5:
    -5x+y = -27
    +5x-7y = 69
    Sum: -6y = 42
    Y = -7

    In Eq5, replace y with -7:
    5x-7*-7 = 69
    5x+49 = 69
    5x=20
    X = 4

    In Eq1, replace x with 4, y with -7 and
    solve for z:
    3*4-2*-7+2z = 30
    12+14+2z = 30
    2z = 30-26 = 4
    Z = 2.

    SOLUTION SET: X = 4, Y = -7, Z = 2.




















































    Y =
    =

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