Matematika

Pertanyaan

tolong diisibersama caranya ya!!!!
3x-7y-19=0
5x-2y-8=0
dijwb dgn metode eliminasi,substitusi,dan metode gabungan antara eliminasi dan substitusi...
dibantu ya

1 Jawaban

  • 3x - 7y - 19 = 0
    5x - 2y - 8 = 0
    a) Eliminasi
    * Untuk mencari y
    => 3x - 7y = 19.............(dikali 5)
         5x - 2y = 8..............(dikali 3)

    =>15x - 35y = 95
        15x - 6y = 24 _
         -29y = 71
           y = -71/29

    * Untuk mencari x
    => 3x - 7y = 19...............(dikali 2)
         5x - 2y = 8................(dikali 7)

    => 6x - 14y = 38
        35x - 14y = 56 _
       -29x = -18
           x = -18/-29 = 18/29

    b) Substitusi
    => 3x - 7y = 19..............(persamaan 1)
         5x - 2y = 8...............(persamaan 2)

    Persamaan 1 => 3x - 7y = 19
                             -7y = -3x + 19
                               y = -3/-7 x + 19/-7
                               y = 3/7 x - 19/7

    Substitusi persamaan y= 3/7 x - 19/7 ke persamaan 5x - 2y = 8
    => 5x - 2y = 8
    = 5x - 2 (3/7 x - 19/7) = 8
    = 5x -6/7 x + 38/7 = 8
    29/7 x + 38/7 = 8
    29/7 x = 8 - 38/7 = 18/7
    x = 18/7  = 126/29 = 18/29
          29/7

    Substitusi nilai x ke persamaan 1
    => 3x - 7y = 19
    = 3 (18/29) - 7y = 19
    = 54/29 - 7y = 19
    = -7y = 19 - 54/29 = 497/29
    = y = 497/29
                 -7
     y = 497/203 = -71/29

    c) Eliminasi dan substitusi
    =>3x - 7y = 19.............(dikali 5)
         5x - 2y = 8..............(dikali 3)

    =>15x - 35y = 95
        15x - 6y = 24 _
         -29y = 71
           y = -71/29

    Substitusi nilai y = -71/29 ke persamaan 3x - 7y = 19
    => 3x - 7y = 19
    = 3x - 7 (-71/29) = 19
    = 3x + 497/29 = 19
    3x = 19 - 497/29 = 54/29
    x = 54/29 = 54/87 = 18/29
             3

    Semoga bermanfaat ^_^

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