Matematika

Pertanyaan

tentukan hasil penyelesaian dari 1. 4x+y=8 dan x+2y=10. 2. x=y+2 dan y=2x-5. 3. 2x-3y=11 dan 3x+y=0. 4. 2x+3y=0 dan x+y=1. 5. 4x+3y=6 dan 2x-y=3. tentukan dengan menggunakan metode eliminasi

1 Jawaban

  • 1) 4x + y = 8 |×2
    x + 2y = 10
    maka
    8x + 2y = 16
    x + 2y = 10
    ------------------(-)
    7x = 6
    x = 6/7
    • 4x + y = 8
    x + 2y = 10 |×4
    maka
    4x + y = 8
    4x + 8y = 40
    ------------------(-)
    - 7y = - 32
    y = 32/7
    hp = ( 6/7 , 32/7 )

    2) x = y + 2
    x - y = 2
    y = 2x - 5
    2x - y = 5
    x - y = 2
    --------------(-)
    x = 3
    • 2x - y = 5
    x - y = 2 |×2
    maka
    2x - y = 5
    2x - 2y = 4
    -----------------(-)
    y = 1
    hp = ( 3,1 )

    3) 2x - 3y = 11
    3x + y = 0 |×3
    maka
    2x - 3y = 11
    9x + 3y = 0
    ------------------(+)
    11x = 11
    x = 1
    • 2x - 3y = 11 |×3
    3x + y = 0 |×2
    maka
    6x - 9y = 33
    6x + 2y = 0
    ------------------(-)
    - 11y = 33
    y = - 3
    hp = ( 1 , - 3)

    4) 2x + 3y = 0
    x + y = 1 |×2
    maka
    2x + 3y = 0
    2x + 2y = 2
    ------------------(-)
    y = - 2
    • 2x + 3y = 0
    x + y = 1 |×3
    maka
    2x + 3y = 0
    3x + 3y = 3
    ----------------(-)
    - x = - 3
    x = 3
    hp = ( 3,-2)

    5) 4x + 3y = 6
    2x - y = 3 |×2
    maka
    4x + 3y = 6
    4x - 2y = 6
    ----------------(-)
    5y = 0
    y = 0
    • 4x + 3y = 6
    2x - y = 3 |×3
    maka
    4x + 3y = 6
    6x - 3y = 9
    -----------------(+)
    10x = 15
    x = 15/10
    x = 3/2
    hp = ( 3/2 , 0)

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