tolong yang bisa bantu pake caranya : 1. penyelesaian dari 1/x + 1/y + 1/z = 3 3/x - 2/y - 4/z = -3 2/x + 1/y - 4/z = -1 nilai x + y + z , adalah

Mapel : Matematika
Bab : Sistem Persamaan Linear Tiga Variabel

Diketahui :
- 1/x + 1/y + 1/z = 3
- 3/x - 2/y - 4/z = - 3
- 2/x + 1/y - 4/z = - 1
- 1/x = a
- 1/y = b
- 1/z = c
- a + b + c = 3
- 3a - 2b - 4c = - 3
- 2a + b - 4c = - 1

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

Penyelesaian :
- Nilai x :
a + b + c = 3
c = 3 - a - b

3a - 2b - 4c = - 3
3a - 2b - 4(3 - a - b) = - 3
3a - 2b - 12 + 4a + 4b = - 3
3a + 4a - 2b + 4b = - 3 + 12
7a + 2b = 9

2a + b - 4c = - 1
2a + b - 4(3 - a - b) = - 1
2a + b - 12 + 4a + 4b = - 1
2a + 4a + b + 4b = - 1 + 12
6a + 5b = 11

(7a + 2b = 9) × 5
(6a + 5b = 11) × 2

35a + 10b = 45
12a + 10b = 22
___________ —
23a = 23
a = 23/23
a = 1

1/x = a
1/x = 1
1 = 1 × x
1 = x
x = 1

- Nilai y :
7a + 2b = 9
7 + 2b = 9
2b = 9 - 7
2b = 2
b = 2/2
b = 1

1/y = b
1/y = 1
1 = 1 × y
1 = y
y = 1

- Nilai z :
c = 3 - a - b
c = 3 - 1 - 1
c = 1

1/z = c
1/z = 1
1 = 1 × z
1 = z
z = 1

- Nilai x + y + z :
x + y + z
= 1 + 1 + 1
= 3

Maaf Kalau Salah