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Penjelasan dengan langkah-langkah:

SPLTV

x – 3y + 4z = 4 –> persamaan ke 1

2x + 2y – 4z = 2 —> persamaan ke 2

3x – 2y + z = 3 —> persamaan ke 3

Metode eliminasi :

• Eliminasi persamaan 1 dan 2

x – 3y + 4z = 4 |×2|

2x + 2y – 4z = 2 |×1|

2x – 6y + 8z = 8

2x + 2y – 4z = 2

______________ _

-8y + 12z = 6

-4y + 6z = 3

•Eliminasi persamaan ke 2 dan 3

2x + 2y – 4z = 2 |×3|

3x – 2y + z = 3 |×2|

6x + 6y – 12z = 6

6x – 4y + 2z = 6

_____________ _

10y – 14z = 0

5y – 7z = 0

• Eliminasi pada :

-4y + 6z = 3 |×5|

5y – 7z = 0 |×-4|

-20y + 30z = 15

-20y + 28z = 0

_____________ _

2z = 15

z = 15/2

• substitusi z = 15/2 ke :

5y – 7z = 0

5y = 0 + 7z

5y = 7(15/2)

5y = 105/2

y = 105/2 : 5/1

y = 105/2 × 1/5

y = 105/10

y = 21/2

….

subsitusi y = 21/2 ke :

3x – 2y + z = 3

3x – 2(21/2) + 15/2 = 3

3x – 42/2 + 15/2 = 3

3x – 27/2 = 3

3x = 3 + 27/2

3x = (6 + 27)/2

3x = 33/2

x = 33/2 : 3/1

x = 33/2 × 1/3

x = 33/6

x = 11/2

…

HP = {( 11/2 , 21/2, 15/2)

Pembuktian :

x – 3y +4z = 4

11/2 – 3(21/2) + 4(15/2) = 4

11/2 – 63/2 + 60/2 = 4

8/2 = 4

4 = 4

2x + 2y – 4z = 2

2(11/2) + 2(21/2) – 4(15/2) = 2

11 + 21 – 30 = 2

2 = 2

•Detail jawaban

Mapel : Matematika

Materi : SPLTV (Sistem Persamaan Liniear Tiga Variabel )