6 B + 2 C = 28
7 B + 3 C = 36
Fill in the blanks.
- 1 B + 1 C = _____
- 1 B = _____
- 1 C = _____
(a)
6 B + 2 C = 28 --- (1)
7 B + 3 C = 36 --- (2)
(2) - (1)
(7 B + 3 C) - (6 B + 2 C) = 36 - 28
7 B - 6 B + 3 C - 2 C = 8
1 B + 1 C = 8 --- (3)
1 B + 1 C = 8
(b)
Make C the same.
LCM of 1 and 2 = 2
(3) x 2
2 B + 2 C = 16 --- (4)
(1) - (4)
(6 B + 2 C) - (2 B + 2 C) = 28 - 16
6 B - 2 B + 2 C - 2 C = 12
4 B = 12
1 B = 12 ÷ 4 = 3
(c)
Substitute 1 B = 3 into (3).
1 B + 1 C = 8
3 + 1 C = 8
1 C = 8 - 3 = 5
Answer(s): (a) 8; (b) 3; (c) 5