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MathematicsMathematics
21 January, 02:28

Solution for:

-x + 3y - 2z = 19

2x + y - z = 5

-3x - y + 2z = - 7

+2
Answers (1)
  1. 21 January, 05:30
    0
    x = - 1, y = 4, z = - 3

    Step-by-step explanation:

    Solve the following system:

    {-x + 3 y - 2 z = 19 | (equation 1)

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

    -3 x - y + 2 z = - 7 | (equation 3)

    Swap equation 1 with equation 3:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

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

    -x + 3 y - 2 z = 19 | (equation 3)

    Add 2/3 * (equation 1) to equation 2:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

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

    -x + 3 y - 2 z = 19 | (equation 3)

    Multiply equation 2 by 3:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

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

    -x + 3 y - 2 z = 19 | (equation 3)

    Subtract 1/3 * (equation 1) from equation 3:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

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

    0 x + (10 y) / 3 - (8 z) / 3 = 64/3 | (equation 3)

    Multiply equation 3 by 3/2:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

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

    0 x+5 y - 4 z = 32 | (equation 3)

    Swap equation 2 with equation 3:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

    0 x+5 y - 4 z = 32 | (equation 2)

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

    Subtract 1/5 * (equation 2) from equation 3:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

    0 x+5 y - 4 z = 32 | (equation 2)

    0 x+0 y + (9 z) / 5 = (-27) / 5 | (equation 3)

    Multiply equation 3 by 5/9:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

    0 x+5 y - 4 z = 32 | (equation 2)

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

    Add 4 * (equation 3) to equation 2:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

    0 x+5 y+0 z = 20 | (equation 2)

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

    Divide equation 2 by 5:

    { - (3 x) - y + 2 z = - 7 | (equation 1)

    0 x+y+0 z = 4 | (equation 2)

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

    Add equation 2 to equation 1:

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

    0 x+y+0 z = 4 | (equation 2)

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

    Subtract 2 * (equation 3) from equation 1:

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

    0 x+y+0 z = 4 | (equation 2)

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

    Divide equation 1 by - 3:

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

    0 x+y+0 z = 4 | (equation 2)

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

    Collect results:

    Answer: {x = - 1, y = 4, z = - 3
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