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13 February, 22:16

Solve the system by substitution method

3x+2y+z=-2

-x-y-2z=2

2y+z=-1

+1
Answers (1)
  1. 14 February, 01:19
    0
    First take the first equation

    3x + 2y + z = - 2

    then subtract z

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

    simplify

    3x + 2y = - 2 - z

    add 2

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

    simplify

    3x + 2y + 2 = - z

    divide by - 1

    -3x - 2y - 2 = z

    plug z into last equation

    2y + (-3x - 2y - 2) = - 1

    simplify

    -3x - 2 = - 1

    add 2

    -3x = 1

    divide by - 3

    x = - 1/3

    plug x and z into second equation

    - (-1/3) - y - 2 (-3 (-1/3) - 2y - 2) = 2

    simplify

    1/3 - y - 2 (1 - 2y - 2) = 2

    distribute

    1/3 - y - 2 + 4y + 4 = 2

    combine like terms

    2 1/3 + 3y = 2

    subtract 2 1/3

    3y = - 1/3

    divide by 3

    y = - 1/9

    plug in x and y into second equation

    - (-1/3) - (-1/9) - 2z = 2

    simplify

    1/3 + 1/9 - 2z = 2

    add

    4/9 - 2z = 2

    subtract

    -2z = 14/9

    divide

    z = - 7/9

    answer:

    x = - 1/3

    y = - 1/9

    z = - 7/9
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