Penjelasan dengan langkah-langkah:

Dik.

x + 2y + 3z = 5 ...pers.1

2x - 5y + z = -3 ...pers.2

2x + y - 3z = 13 ...pers.3

Dit ?

2x +3y + z =

Subtitusi pers.1 dan 3

x + 2y + 3z = 5

2x + y - 3z = 13

____________ +

3x + 3y = 18 ..pers.4

Subtitusi pers.2 dan 3

2x - 5y + z = -3

2x + y - 3z = 13

_____________ -

-6y + 4z = -16 ...pers.5

Subtitusi pers.1 dan 2

x + 2y + 3z = 5 | × 5 |

2x - 5y + z = -3 | × 2 l

5x + 10y + 15z = 25

4x - 10y + 2z = -6

______________ +

9x + 17z = 19 pers.6

Subtitusi pers.4 dan 6

3x + 3y = 18 | × 3 |

9x + 17z = 19 | × 1 |

9x + 9y = 54

9x + 17z = 19

__________ -

9y - 17z = 35 ...pers.7

Subtitusi pers.5 dan 7

-6y + 4z = -16 | × 9 |

9y - 17z = 35 | × 6 |

-54y + 36z = -144

54y - 102z = 210

______________ +

-66z = 66

z = 66/-66

z = -1

Masukan nilai z ke pers.5

-6y + 4z = -16

-6y + 4(-1) = -16

-6y - 4 = -16

-6y = -16 + 4

-6y = -12

y = -12/-6

y = 2

Masukan nilai z = -1 ke pers.

9x + 17z = 19

9x + 17(-1) = 19

9x - 17 = 19

9x = 19 + 17

9x = 36

x = 36/9

x = 4

Buktikan bahwa nilai x = 4 , y = 2 ,dan z = -1 benar dengan memasukkan nilai pada masing-masing persamaan :

x + 2y + 3z = 5

4 + 2(2) + 3(-1) = 5

4 + 4 -3 = 5 (benar)

2x -5y + z = -3

2(4) - 5(2) - 1 = -3

8 - 10 - 1 = -3 (benar)

2x + y - 3z = 13

2(4) + 2 - 3(-1) = 13

8 + 2 + 3 = 13

Jadi nilai

2x + 3y + z =

2(4) + 3(2) -1 =

8 + 6 - 1 = 13

Semoga membantu