tentukan himpunan penyelesaian dari 1/x+1/y=-1/6 dan 2/x-3/y=2 1/6

Mapel : Matematika
Bab : Sistem Persamaan Linear Dua Variabel

Diketahui :
- 1/x + 1/y = - 1/6
- 2/x - 3/y = 2 1/6
- 1/x = a
- 1/y = b
- a + b = - 1/6
- 2a - 3b = 2 1/6

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

Penyelesaian :
- Nilai x :
a + b = - 1/6
b = - 1/6 - a

2a - 3b = 2 1/6
2a - 3(- 1/6 - a) = 13/6
2a + 3/6 + 3a = 13/6
2a + 3a = 13/6 - 3/6
5a = 10/6
a = 10/6 ÷ 5
a = 10/6 × 1/5
a = 2/6 × 1/1
a = 2/6
a = 1/3

1/x = a
1/x = 1/3
x = 3

- Nilai y :
b = - 1/6 - a
b = - 1/6 - 1/3
b = - 1/6 - 2/6
b = - 3/6
b = - 1/2

1/y = - 1/2
- y = 2
y = - 2

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