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9 March, 23:06

Solve the system by elimination. (show your work)

-2x + 2y + 3z = 0

-2x - y + z = - 3

2x + 3y + 3z = 5

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Answers (1)
  1. 9 March, 23:18
    0
    x = 1, y = 1, z = 0

    Step-by-step explanation by elimination:

    Solve the following system:

    {-2 x + 2 y + 3 z = 0 | (equation 1)

    -2 x - y + z = - 3 | (equation 2)

    2 x + 3 y + 3 z = 5 | (equation 3)

    Subtract equation 1 from equation 2:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x - 3 y - 2 z = - 3 | (equation 2)

    2 x + 3 y + 3 z = 5 | (equation 3)

    Multiply equation 2 by - 1:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+3 y + 2 z = 3 | (equation 2)

    2 x + 3 y + 3 z = 5 | (equation 3)

    Add equation 1 to equation 3:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+3 y + 2 z = 3 | (equation 2)

    0 x+5 y + 6 z = 5 | (equation 3)

    Swap equation 2 with equation 3:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+5 y + 6 z = 5 | (equation 2)

    0 x+3 y + 2 z = 3 | (equation 3)

    Subtract 3/5 * (equation 2) from equation 3:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+5 y + 6 z = 5 | (equation 2)

    0 x+0 y - (8 z) / 5 = 0 | (equation 3)

    Multiply equation 3 by 5/8:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+5 y + 6 z = 5 | (equation 2)

    0 x+0 y - z = 0 | (equation 3)

    Multiply equation 3 by - 1:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+5 y + 6 z = 5 | (equation 2)

    0 x+0 y+z = 0 | (equation 3)

    Subtract 6 * (equation 3) from equation 2:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+5 y+0 z = 5 | (equation 2)

    0 x+0 y+z = 0 | (equation 3)

    Divide equation 2 by 5:

    { - (2 x) + 2 y + 3 z = 0 | (equation 1)

    0 x+y+0 z = 1 | (equation 2)

    0 x+0 y+z = 0 | (equation 3)

    Subtract 2 * (equation 2) from equation 1:

    { - (2 x) + 0 y+3 z = - 2 | (equation 1)

    0 x+y+0 z = 1 | (equation 2)

    0 x+0 y+z = 0 | (equation 3)

    Subtract 3 * (equation 3) from equation 1:

    { - (2 x) + 0 y+0 z = - 2 | (equation 1)

    0 x+y+0 z = 1 | (equation 2)

    0 x+0 y+z = 0 | (equation 3)

    Divide equation 1 by - 2:

    {x+0 y+0 z = 1 | (equation 1)

    0 x+y+0 z = 1 | (equation 2)

    0 x+0 y+z = 0 | (equation 3)

    Collect results:

    Answer: {x = 1, y = 1, z = 0
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