Matematika

Pertanyaan

1. Himpunan penyelesaian dari persamaan {x - y + z = 3
{2x + y - 3z = -5
{3x + 2y + z = 16
Adalah....

2. penyelesaian dari sistem persamaan {x + y - z = -3
{ x + 2y + z = 7
{2x + y + z = 4
Adalah....

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1 Jawaban

  • 1) x - y + z = 3 |×3
    2x + y - 3z = - 5 |×1
    3x - 3y + 3z = 9
    2x + y - 3z = - 5
    ------------------------(+)
    5x - 2y = 4 ... pers 1

    2x + y - 3z = - 5 |×1
    3x + 2y + z = 16 |×3
    2x + y - 3z = - 5
    9x + 6y + 3z = 48
    --------------------------(+)
    11x + 7y = 43 ... pers 2

    pers 1 & 2
    5x - 2y = 4 |×7
    11x + 7y = 43 |×2
    35x - 14y = 28
    22x + 14y = 86
    -----------------------(+)
    57x = 114
    x = 2

    5x - 2y = 4
    5(2) - 2y = 4
    10 - 2y = 4
    - 2y = 4 - 10
    - 2y = - 6
    y = 3

    x - y + z = 3
    2 - 3 + z = 3
    - 1 + z = 3
    z = 3 + 1
    z = 4

    2) x + y - z = - 3
    x + 2y + z = 7
    ------------------------(+)
    2x + 3y = 4 ... pers 1

    x + 2y + z = 7
    2x + y + z = 4
    ----------------------(-)
    - x + y = 3 ... pers 2

    pers 1 & 2
    2x + 3y = 4 |×1
    -x + y = 3 |×2
    2x + 3y = 4
    - 2x + 2y = 6
    ------------------- (+)
    5y = 10
    y = 2

    2x + 3y = 4
    2x + 3(2) = 4
    2x + 6 = 4
    2x = 4 - 6
    2x = - 2
    x = - 1

    x + 2y + z = 7
    - 1 + 2(2) + z = 7
    - 1 + 4 + z = 7
    3 + z = 7
    z = 7 - 3
    z = 4

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