Tentukan himpunan penyelesaian dari sistem persamaan x+y+z=4 5x+4y+z=6 8x+10y+z=15

Mapel : Matematika
Bab : Sistem Persamaan Linear Tiga Variabel

Diketahui :
- x + y + z = 4
- 5x + 4y + z = 6
- 8x + 10y + z = 15

Ditanya :
- Nilai x = ......?
- Nilai y = ......?
- Nilai z = ......?

Penyelesaian :
- Nilai x :
x + y + z = 4
z = 4 - x - y

5x + 4y + z = 6
5x + 4y + 4 - x - y = 6
5x - x + 4y - y = 6 - 4
4x + 3y = 2

8x + 10y + z = 15
8x + 10y + 4 - x - y = 15
8x - x + 10y - y = 15 - 4
7x + 9y = 11

(4x + 3y = 2) × 3
(7x + 9y = 11) × 1

12x + 9y = 6
7x + 9y = 11
—————— —
5x = - 5
x = - 5/5
x = - 1

- Nilai y :
4x + 3y = 2
4(- 1) + 3y = 2
- 4 + 3y = 2
3y = 2 + 4
3y = 6
y = 6/3
y = 2

- Nilai z :
z = 4 - x - y
z = 4 - (- 1) - 2
z = 4 + 1 - 2
z = 5 - 2
z = 3

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