Matematika

Pertanyaan

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1 Jawaban

  • No. 2

    x + y - z = 1 ............(1)
    2x + y + z = 11.........(2)
    x + 2y + z = 12.........(3)

    dari (1) dan (2)
    x + y - z = 1
    2x + y + z = 11
    ---------------------- (+)
    3x + 2y = 12.................(4)

    dari (1) dan (3)
    x + y - z = 1
    x + 2y + z = 12
    --------------------- (+)
    2x + 3y = 13.................(5)

    dari (4) dan (5)
    9x + 6y = 36
    4x + 6y = 26
    ----------------- (-)
    5x = 10
    x = 2

    subtitusi
    2x + 3y = 13
    2(2) + 3y = 13
    3y = 13 - 4
    3y = 9
    y = 3

    subtitusi
    x + y - z = 1
    2 + 3 - z = 1
    z = 5 - 1
    z = 4

    HP = {(2,3,4)}

    No. 3
    2x + y + z = 4700 ....................(1)
    x + 2y + z = 4300 ....................(2)
    3x + 2y + z = 7100 ..................(3)

    dari (1) dan (2)
    2x + y + z = 4700
    x + 2y + z = 4300
    ------------------------- (-)
    x - y = 400 ....................(4)

    dari (1) dan (3)
    2x + y + z = 4700
    3x + 2y + z = 7100
    --------------------------- (-)
    x + y = 2400 ..................(5)

    dari (4) dan (5)
    x - y = 400
    x + y = 2400
    ------------------ (+)
    2x = 2800
    x = 1400

    subtitusi
    x - y = 400
    1400 - y = 400
    y = 1000

    subtitusi
    2x + y + z = 4700
    2(1400) + 1000 + z = 4700
    z = 4700 - 3800
    z = 900

    jadi harga
    buku tulis = 1400
    ppensil = 1000
    penghapus = 900

    No. 4
    misalkan
    m = 1/x
    n = 1/y
    r = 1/z
    maka
    m + n = 2 ...........(1)
    n - r = -3 ............(2)
    m - r = 2 .............(3)

    dari (1) dan (2)
    m + n = 2
    n - r = -3
    ------------ (-)
    m + r = 5 ..........(4)

    dari (3) dan (4)
    m - r = 2
    m + r = 5
    --------------- (+)
    2m = 7
    m = 7/2

    m - r = 2
    m + r = 5
    --------------- (-)
    2r = 3
    r = 3/2

    subtitusi
    m + n = 2
    7/2 + n = 4/2
    n = -3/2

    jadi
    m = 1/x
    7/2 = 1/x
    x = 2/7

    n = -3/2
    1/y = -3/2
    y = -2/3

    r = 3/2
    1/z = 3/2
    z = 2/3

    jadi 
    x + y + z
    = (2/7) + (-2/3) + (2/3)
    = 2/7

    No. 6
    x = 2
    y = 1 , maka
    2a - b = 6 .............(1)
    4a + 3b = 2 ...........(2)

    eliminasi
    4a - 2b = 12
    4a + 3b = 2
    ----------------- (-)
    -5b = 10
    b = -2

    subtitusi
    2a - b = 6
    2a + 2 = 6
    2a = 4
    a = 2

    a² + b²
    = (2)² + (2)²
    = 4 + 4
    = 8