2x + y - 3z = -1 2x + 2y + z = 10 x - y + 3z = 1 tentukan himpunan penyelesainnya!

Mapel : Matematika
Bab : Sistem Persamaan Linear Tiga Variabel

Diketahui :
- 2x + y - 3z = - 1
- 2x + 2y + z = 10
- x - y + 3z = 1

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

Penyelesaian :
- Nilai x :
2x + 2y + z = 10
z = 10 - 2x - 2y

2x + y - 3z = - 1
2x + y - 3(10 - 2x - 2y) = - 1
2x + y - 30 + 6x + 6y = - 1
2x + 6x + y + 6y = - 1 + 30
8x + 7y = 29

x - y + 3z = 1
x - y + 3(10 - 2x - 2y) = 1
x - y + 30 - 6x - 6y = 1
x - 6x - y - 6y = 1 - 30
- 5x - 7y = - 29

8x + 7y = 29
- 5x - 7y = - 29
___________ +
3x = 0
x = 0

- Nilai y :
8x + 7y = 29
0 + 7y = 29
7y = 29
y = 29/7
y = 4 1/7

- Nilai z :
z = 10 - 2x - 2y
z = 10 - 0 - 2(29/7)
z = 10 - 58/7
z = 12/7
z = 1 5/7

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