Diketahui SPLTV berikut 2a-3b=2 4a+5c=5 6b-10c=-3 Himpunan penyelesaian SPLTV tersebut adalah

Diketahui :
- 2a - 3b = 2
- 4a + 5c = 5
- 6b - 10c = - 3

Ditanya : Nilai a, b, dan c = .....?

Penyelesaian :
- Nilai a :
6b - 10c = - 3
- 10c = - 3 - 6b
10c = 3 + 6b
c = 3/10 + 6/10b

4a + 5c = 5
4a + 5(3/10 + 6/10b) = 5
4a + 15/10 + 3b = 5
10(4a + 15/10 + 3b = 5)
40a + 15 + 30b = 50
40a + 30b = 50 - 15
40a + 30b = 35
1/5(40a + 30b = 35)
8a + 6b = 7

(8a + 6b = 7) × 1
(2a - 3b = 2) × 2

8a + 6b = 7
4a - 6b = 4
________ +
12a = 11
a = 11/12

- Nilai b :
2a - 3b = 2
2(11/12) - 3b = 2
22/12 - 3b = 2
12(22/12 - 3b = 2)
22 - 36b = 24
- 36b = 24 - 22
- 36b = 2
b = 2/- 36
b = - 1/18

- Nilai c :
c = 3/10 + 6/10b
c = 3/10 + 6/10(- 1/18)
c = 3/10 - 1/30
c = 3 × 3 - 1/30
c = 9 - 1/30
c = 8/30
c = 4/15

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