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9 August, 11:05

Solve the following System of Equations

5x+4y-z=1

2x-2y+z=1

-x-y+z=2

+5
Answers (1)
  1. 9 August, 12:13
    0
    x = 0, y = 1, z = 3

    Step-by-step explanation:

    Solve the following system:

    {5 x + 4 y - z = 1 | (equation 1)

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

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

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

    {5 x + 4 y - z = 1 | (equation 1)

    0 x - (18 y) / 5 + (7 z) / 5 = 3/5 | (equation 2)

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

    Multiply equation 2 by 5:

    {5 x + 4 y - z = 1 | (equation 1)

    0 x - 18 y + 7 z = 3 | (equation 2)

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

    Add 1/5 * (equation 1) to equation 3:

    {5 x + 4 y - z = 1 | (equation 1)

    0 x - 18 y + 7 z = 3 | (equation 2)

    0 x - y/5 + (4 z) / 5 = 11/5 | (equation 3)

    Multiply equation 3 by 5:

    {5 x + 4 y - z = 1 | (equation 1)

    0 x - 18 y + 7 z = 3 | (equation 2)

    0 x - y + 4 z = 11 | (equation 3)

    Subtract 1/18 * (equation 2) from equation 3:

    {5 x + 4 y - z = 1 | (equation 1)

    0 x - 18 y + 7 z = 3 | (equation 2)

    0 x+0 y + (65 z) / 18 = 65/6 | (equation 3)

    Multiply equation 3 by 18/65:

    {5 x + 4 y - z = 1 | (equation 1)

    0 x - 18 y + 7 z = 3 | (equation 2)

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

    Subtract 7 * (equation 3) from equation 2:

    {5 x + 4 y - z = 1 | (equation 1)

    0 x - 18 y+0 z = - 18 | (equation 2)

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

    Divide equation 2 by - 18:

    {5 x + 4 y - z = 1 | (equation 1)

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

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

    Subtract 4 * (equation 2) from equation 1:

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

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

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

    Add equation 3 to equation 1:

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

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

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

    Divide equation 1 by 5:

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

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

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

    Collect results:

    Answer: {x = 0, y = 1, z = 3
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