Rabu, April 17, 2024
Matematika

Selesaikanlah setiap sistem persamaan berikut

(soal 1) Selesaikanlah setiap sistem persamaan berikut.

Selesaikanlah setiap sistem persamaan berikut
(Soal 1) Selesaikanlah setiap sistem persamaan berikut.

Pembahasan

Nomor (1)

  • 3x – y = 2
  • x + y = 6
  • ____________+
  • 4x = 8
  • x = \frac {8} {4} = 2
  • Subtitusi x = 2 ke persamaan x + y = 6
  • 2 + y = 6
  • y = 6 – 2 = 4
  • Jadi jawabannya: (2, 4)

Nomor (2)

  • x + 4y = 9
  • x + y = 3
  • ___________ –
  • 3y = 6
  • y = \frac {6} {3} = 2
  • Subtitusi y = 2 ke persamaan x + y = 3
  • x + 2 = 3
  • x = 3 – 2 = 1
  • Jadi jawabannya: (1, 2)

Nomor (3)

  • 3x – 2y = -13
  • -3x + 4y = 23
  • _______________ +
  • 2y = 10
  • y = \frac {10} {2} = 5
  • Subtitusi y = 5 ke persamaan 3x – 2y = -13
  • 3x – 2 . 5 = -13
  • 3x – 10 = -13
  • 3x = -13 + 10 = -3
  • x = \frac {-3} {3} = -1
  • Jadi jawabannya: (-1, 5)

Nomor (4)

  • 2x – y = -4
  • x – y = -1
  • ____________-
  • x = -3
  • Subtitusi x = -3 ke persamaan x – y = -1
  • -3 – y = -1
  • y = -3 + 1 = -2
  • Jadi jawabannya: (-3, -2)

(soal 2) Selesaikanlah setiap sistem persamaan berikut.

Selesaikanlah setiap sistem persamaan berikut
(soal 2) Selesaikan setiap sistem persamaan berikut

Pembahasan

Nomor (1)

  • 2x – 3y = 12 (x 1)
  • 3x + y = 7 (x 3)
  • 2x – 3y = 12
  • 9x + 3y = 21
  • _______________+
  • 11x = 33
  • x = \frac {33} {11} = 3
  • Subtitusi x = 3 ke persamaan 2x – 3y = 12
  • 2 . 3 – 3y = 12
  • 6 – 3y = 12
  • 3y = 6 – 12 = -6
  • y = \frac {-6} {3} = -2
  • Jadi jawabannya: (3, -2)

Nomor (2)

  • 3x – 4y = 10 (x 2)
  • 5x – 8y = 22 (x 1)
  • 6x – 8y = 20
  • 5x – 8y = 22
  • ______________-
  • x = -2
  • Subtitusi x = -2 ker persamaan 3x – 4y = 10
  • 3 . (-2) – 4y = 10
  • -6 – 4y = 10
  • 4y = -6 – 10 = -16
  • y = \frac {-16} {4} = -4
  • Jadi jawabannya: (-2, -4)

Nomor (3)

  • -2x + 3y = -9 (x 2)
  • 4x – 5y = 15 (x 1)
  • -4x + 6y = -18
  • 4x – 5y = 15
  • ________________+
  • y = -3
  • Subtitusi y = -3 ke persamaan 4x – 5y = 15
  • 4x – 5 . (-3) = 15
  • 4x + 15 = 15
  • 4x = 15 – 15 = 0
  • x = \frac {0} {4} = 0
  • Jadi jawabannya: (0, -3)

(soal 3) Selesaikanlah setiap sistem persamaan berikut.

Selesaikanlah setiap sistem persamaan berikut

Pembahasan

Nomor (1)

  • 2x + 3y = 8 (x 3)
  • 3x – 4y = -5 (x 2)
  • 6x + 9y = 24
  • 6x – 8y = -10
  • ______________-
  • 17y = 34
  • y = \frac {34} {17} = 2
  • Subtitusi y = 2 ke persamaan 2x + 3y = 8
  • 2x + 3 . 2 = 8
  • 2x + 6 = 8
  • 2x = 8 – 6 = 2
  • x = \frac {2} {2} = 1
  • Jadi jawabannya: (1, 2)

Nomor (2)

  • 3x – 2y = 13 (x 4)
  • 4x + 5y = 2 (x 3)
  • 12x – 8y = 52
  • 12x + 15y = 6
  • ________________-
  • -23x = 46
  • x = \frac {46} {-23} = -2
  • Subtitusi x = -2 ke persamaan 3x – 2y = 13
  • 3 . (-2) – 2y = 13
  • -6 – 2y = 13
  • 2y = -6 – 13
  • 2y = – 19
  • y = \frac {-19} {2}
  • Jadi jawabannya: (-2, – \frac {19} {2})

Nomor (3)

  • 7x – 3y = -5 (x 5)
  • 6x – 5y = 3 (x 3)
  • 35x – 15y = -25
  • 18x – 15y = 9
  • _________________-
  • 17x = -34
  • x = \frac {-34} {17} = -2
  • Subtitusi x = -2 ke persamaan 7x – 3y = -5
  • 7 . (-2) – 3y = -5
  • -14 – 3y = -5
  • 3y = -14 + 5 = -9
  • y = \frac {-9} {3} = -3
  • Jadi jawabannya: (-2, -3)

Nomor (4)

  • 4x + 8y = 7 (x 6)
  • 6x + 5y = 7 (x 4)
  • 24x + 48y = 42
  • 24x + 20y = 28
  • __________________-
  • 28y = 14
  • y = \frac {14} {28} = \frac {1} {2}
  • Subtitusi y = \frac {1} {2} ke persamaan 4x + 8y = 7
  • 4x + 8 . \frac {1} {2} = 7
  • 4x + 4 = 7
  • 4x = 7 – 4 = 3
  • x = \frac {3} {4}
  • Jadi jawabannya: (\frac {1} {2}, \frac {3} {4})

(soal 4) Selesaikanlah sistem persamaan berikut menggunakan metode subtitusi.

Selesaikanlah sistem persamaan berikut menggunakan metode subtitusi.

Pembahasan

Nomor (1)

  • Subtitusi x = 3y + 1 ke persamaan x + 2y = 11
  • (3y + 1) + 2y = 11
  • 5y = 11 – 1
  • 5y = 10
  • y = \frac {10} {5} = 2
  • Subtitusi y = 2 ke persamaan x = 3y + 1
  • x = 3 . 2 + 1 = 6 + 1 = 7
  • Jadi jawabannya: (7, 2)

Nomor (2)

  • Subtitusi y = 7x – 2 ke persamaan y = 4x + 1
  • 7x – 2 = 4x + 1
  • 7x – 4x = 1 + 2
  • 3x = 3
  • x = \frac {3} {3} = 1
  • Subtitusi x = 1 ke persamaan y = 4x + 1
  • y = 4 . 1 + 1 = 5
  • Jadi jawabannya: (1, 5)

Nomor (3)

  • Subtitusi y = x – 3 ke persamaan x – 2y = 9
  • x – 2 (x – 3) = 9
  • x – 2x + 6 = 9
  • -x = 9 – 6
  • -x = 3
  • x = -3
  • Subtitusi x = -3 ke persamaan y = x – 3
  • y = -3 – 3 = -6
  • Jadi jawabannya: (-3, -6)

Nomor (4)

  • x – 3y = 5
  • x = 5 + 3y kemudian subtitusi ke persamaan 2x + y = 3
  • 2(5 + 3y) + y = 3
  • 10 + 6y + y = 3
  • 7y = 3 – 10
  • 7y = -7
  • y = \frac {-7} {7} = -1
  • Subtitusi y = -1 ke persamaan x – 3y = 5
  • x – 3 . (-1) = 5
  • x + 3 = 5
  • x = 5 – 3 = 2
  • Jadi jawabannya: (2, -1)

(soal 5) Selesaikanlah sistem persamaan berikut dengan metode yang tepat.

Selesaikanlah sistem persamaan berikut dengan metode yang tepat.

Pembahasan

Nomor (1) metode eliminasi dan subtitusi.

  • 3x + y = 7 (x 1)
  • x + 2y = 9 (x 3)
  • 3x + y = 7
  • 3x + 6y = 27
  • _______________-
  • -5y = -20
  • y = \frac {-20} {-5} = 4
  • Subtitusi y = 4 ke persamaan x + 2y = 9
  • x + 2 . 4 = 9
  • x + 8 = 9
  • x = 9 – 8 = 1
  • Jadi jawabannya: (1, 4)

Nomor (2) metode subtitusi

  • Subtitusi x = -y + 2 ke persamaan x + 3y = 3
  • (-y + 2) + 3y = 3
  • 2y = 3 – 2 = 1
  • y = \frac {1} {2}
  • Subtitusi y = \frac {1} {2} ke persamaan x = -y + 2
  • x = – \frac {1} {2} + 2 = \frac {3} {2}
  • Jadi jawabannya: (\frac {3} {2}, \frac {1} {2})

(soal 6) Selesaikanlah sistem persamaan berikut.

Selesaikanlah sistem persamaan berikut

Pembahasan

Nomor (1)

  • 2(x – y) – x = 8
  • 2x – 2y – x = 8
  • x – 2y = 8 … (pers. 1)
  • 5x – (3x – y) = 1
  • 5x – 3x + y = 1
  • 2x + y = 1
  • y = 1 – 2x … (pers 2)
  • Subtitusi y pers. 2 ke pers. 1
  • x – 2 (1 – 2x) = 8
  • x – 2 + 4x = 8
  • 5x = 8 + 2
  • 5x = 10
  • x = \frac {10} {5} = 2
  • Subtitusi x = 2 ke persamaan 1
  • 2 – 2y = 8
  • 2y = 2 – 8 = -6
  • y = \frac {-6} {2} = -3
  • Jadi jawaban: (2, -3)

Nomor (2)

  • 3(x + 2y) = 2(x – 3)
  • 3x + 6y = 2x – 6
  • 6y = 2x – 3x – 6
  • 6y = -x – 6 … (pers. 1)
  • Subtitusi y = 4 – x ke persamaan 1
  • 6(4 – x) = -x – 6
  • 24 – 6x = -x – 6
  • 24 + 6 = -x + 6x
  • 30 = 5x
  • x = \frac {30} {5} = 6
  • Subtitusi x = 6 ke persamaan y = 4 – x
  • y = 4 – 6 = -2
  • Jadi jawaban: (6, -2)

(soal 7) Selesaikanlah sistem persamaan berikut setelah kamu mengubah koefisien-koefisien variabel dalam bilangan bulat.

Selesaikanlah sistem persamaan berikut setelah kamu mengubah koefisien-koefisien variabel dalam bilangan bulat

Pembahasan

Nomor (1)

  • 0,2x + 0,3y = 0,5 (x 10)
  • 2x + 3y = 5 … (pers. 1)
  • x + 5y = -1 (x 2)
  • 2x + 10y = -2 (pers. 2)
  • Eliminasi x pada pers. 1 dan pers. 2
  • 2x + 3y = 5
  • 2x + 10y = -2
  • _______________-
  • -7y = 7
  • y = \frac {7} {-7} = -1
  • Subtitusi y = -1 ke pers . 2
  • x + 5y = -1
  • x + 5 . (-1) = -1
  • x – 5 = -1
  • x = -1 + 5 = 4
  • Jadi jawaban: (4, -1)

Nomor (2)

  • 8x – 3y = 9 … (pers. 1)
  • \frac {1} {6}x + \frac {1} {2} y = 2 (x 6)
  • x + 3y = 12 .. (pers. 2)
  • Eliminasi y pers. 1 dan pers. 2
  • 8x – 3y = 9
  • x + 3y = 12
  • _____________+
  • 9x = 21
  • x = \frac {21} {9} = \frac {7} {3}
  • Subtitusi x = \frac {7} {3} ke pers. 2
  • x + 3y = 12
  • 3y = 12 – x
  • 3y = 12 – \frac {7} {3}
  • 3y = \frac {36} {3}\frac {7} {3} = \frac {29} {3}
  • y = \frac {29} {9}
  • Jadi jawaban: (\frac {7} {3}, \frac {29} {9})

(soal 8) Selesaikanlah setiap sistem persamaan berikut.

Selesaikanlah setiap sistem persamaan berikut

Pembahasan

Nomor (1)

  • x – 3y = 4
  • x + 3y = 10
  • ______________-
  • -2y = -6
  • y = \frac {-6} {-2} = 3
  • Subtitusi y = 3 ke x – 3y = 4
  • x – 3 . 3 = 4
  • x – 9 = 4
  • x = 4 + 9 = 13
  • Jawaban: (13, 4)

Nomor (2)

  • 2x + 5y = -8 (x 2)
  • 4x + 10y = -16
  • 4x + 3y = 12
  • ________________-
  • 7y = -28
  • y = \frac {-28} {7} = 4
  • 2x + 5y = -8
  • 2x + 5 . 4 = -8
  • 2x + 20 = -8
  • 2x = -8 – 20 = -28
  • x = \frac {-28} {2} = -14
  • Jawaban: (-14, 4)

Nomor (3)

  • 2x – 3y = 7 (x 3)
  • 6x – 9y = 21 … (pers. 1)
  • 3x + 2y = 4 (x 2)
  • 6x + 4y = 8 … (pers. 2)
  • Eliminasi x pers. 1 dan pers. 2
  • 6x – 9y =21
  • 6x + 4y = 8
  • _____________-
  • -13y = 13
  • y = \frac {13} {-13} = -1
  • 2x – 3y = 7
  • 2x – 3 . (-1) = 7
  • 2x + 3 = 7
  • 2x = 7 – 3 = 4
  • x = \frac {4} {2} = 2
  • Jawaban: (2, -1)

Nomor (4)

  • 2x + y = -9
  • x = 3y – 1 (subtitusi ke pers di atas)
  • 2(3y – 1) + y = -9
  • 6y – 2 + y = -9
  • 7y = -9 + 2 = -7
  • y = \frac {-7} {7} = -1
  • x = 3y – 1 = 3 . (-1) – 1 = -4
  • Jawaban: (-4, -1)

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