Matematika

Pertanyaan

x - 2y + z = -1
2x + y - 3z = 3
3x + 3y - 2z = 10

tolong bantu ya ..
pakai cara nya

1 Jawaban

  • x - 2y + z = -1 (1)
    2x + y - 3z = 3 (2)
    3x + 3y - 2z = 10 (3)

    eliminasi persamaan (1) dan (2)
    x - 2y + z = -1 |x2| 2x - 4y + 2z = -2
    2x + y - 3z = 3 |x1 | 2x + y - 3z = 3
    ---------------------------------------------------- –
    -5y + 5z = -5 (4)

    eliminasi persamaan (1) dan (3)
    x - 2y + z = -1 |x3| 3x - 6y + 3z = -3
    3x + 3y - 2z = 10 |x1 | 3x + 3y - 2z = 10
    ---------------------------------------------------- –
    -9y + 5z = -13 (5)

    eliminasi persamaan (4) dan (5)
    -5y + 5z = -5
    -9y + 5z = -13
    ---------------------- –
    4y = 8
    y = 2

    substitusi ke persamaan (4)
    -5y + 5z = -5
    -5(2) + 5z = -5
    -10 + 5z = -5
    5z = -5 + 10
    5z = 5
    z = 1

    substitusi ke persamaan (1)
    x - 2y + z = -1
    x -2(2) + 1 = -1
    x - 4 + 1 = -1
    x - 3 = -1
    x = -1 + 3
    x = 2

    jadi HP = {(2,2,1)}
    semoga membantu :)

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