Matematika

Pertanyaan

Tentukan penyelesaian sistem persamaan berikut dengan metode subtitusi, untuk x, y ∈ R !
A. x - 3y = 5 dan 3x +2y = -7
B. 2x +2y = -4 dan 6x - 3y= -18
C. 3x - 2y - 7= 0 dan 4x + y - 13= 0

1 Jawaban

  • a. x - 3y = 5         |x3
       3x + 2y = -7      |x1
    --------------------- (-)
    3x - 9y = 15
    3x + 2y = -7
    ---------------------- (-)
    -11y = 22, y = -1

    3x - 9(-1) = 15
    3x + 9 = 15
    3x = 15-9 = 6
    x = 2
    x,y = {2,-1}

    b. 2x + 2y = -4   |x3
        6x - 3y = -18  |x1
    ---------------------- (-)
    6x + 6y = -12
    6x - 3y = -18
    ---------------------- (-)
    9y = 6, y = 6/9 = 2/3

    2x + 2(2/3) = -4
    2x + 4/3 = -4
    2x = -4 - 4/3 = -12/3 - 4/3 = -16/3
    x = -8/3

    x,y = {-8/3,2/3)

    c. 3x - 2y = 7    |x1
        4x + y = 13   |x2
    --------------------- (+)
    7x = 20, x = 20/7

    3(20/7) - 2y = 7
    60/7 - 2y = 7
    -2y = 7 - 60/7 = 49/7 - 60/7 = -11/7
    y = 11/14

    x,y = {20/7,11/14)

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