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12 November, 11:19

Solve each system of equations

2a-3b+5c=58

-5a+b-4c=-51

-6a-8b+c=22

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Answers (1)
  1. 12 November, 14:06
    0
    a = 3, b = - 4, c = 8

    Step-by-step explanation:

    Solve the following system:

    {2 a - 3 b + 5 c = 58 | (equation 1)

    -5 a + b - 4 c = - 51 | (equation 2)

    -6 a - 8 b + c = 22 | (equation 3)

    Swap equation 1 with equation 3:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    - (5 a) + b - 4 c = - 51 | (equation 2)

    2 a - 3 b + 5 c = 58 | (equation 3)

    Subtract 5/6 * (equation 1) from equation 2:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a + (23 b) / 3 - (29 c) / 6 = - 208/3 | (equation 2)

    2 a - 3 b + 5 c = 58 | (equation 3)

    Multiply equation 2 by 6:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a+46 b - 29 c = - 416 | (equation 2)

    2 a - 3 b + 5 c = 58 | (equation 3)

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

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a+46 b - 29 c = - 416 | (equation 2)

    0 a - (17 b) / 3 + (16 c) / 3 = 196/3 | (equation 3)

    Multiply equation 3 by 3:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a+46 b - 29 c = - 416 | (equation 2)

    0 a - 17 b + 16 c = 196 | (equation 3)

    Add 17/46 * (equation 2) to equation 3:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a+46 b - 29 c = - 416 | (equation 2)

    0 a+0 b + (243 c) / 46 = 972/23 | (equation 3)

    Multiply equation 3 by 46/243:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a+46 b - 29 c = - 416 | (equation 2)

    0 a+0 b+c = 8 | (equation 3)

    Add 29 * (equation 3) to equation 2:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a+46 b+0 c = - 184 | (equation 2)

    0 a+0 b+c = 8 | (equation 3)

    Divide equation 2 by 46:

    { - (6 a) - 8 b + c = 22 | (equation 1)

    0 a+b+0 c = - 4 | (equation 2)

    0 a+0 b+c = 8 | (equation 3)

    Add 8 * (equation 2) to equation 1:

    { - (6 a) + 0 b+c = - 10 | (equation 1)

    0 a+b+0 c = - 4 | (equation 2)

    0 a+0 b+c = 8 | (equation 3)

    Subtract equation 3 from equation 1:

    { - (6 a) + 0 b+0 c = - 18 | (equation 1)

    0 a+b+0 c = - 4 | (equation 2)

    0 a+0 b+c = 8 | (equation 3)

    Divide equation 1 by - 6:

    {a+0 b+0 c = 3 | (equation 1)

    0 a+b+0 c = - 4 | (equation 2)

    0 a+0 b+c = 8 | (equation 3)

    Collect results:

    Answer: {a = 3, b = - 4, c = 8
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