6 B + 2 C = 22
7 B + 3 C = 29
Fill in the blanks.
- 1 B + 1 C = _____
- 1 B = _____
- 1 C = _____
(a)
6 B + 2 C = 22 --- (1)
7 B + 3 C = 29 --- (2)
(2) - (1)
(7 B + 3 C) - (6 B + 2 C) = 29 - 22
7 B - 6 B + 3 C - 2 C = 7
1 B + 1 C = 7 --- (3)
1 B + 1 C = 7
(b)
Make C the same.
LCM of 1 and 2 = 2
(3) x 2
2 B + 2 C = 14 --- (4)
(1) - (4)
(6 B + 2 C) - (2 B + 2 C) = 22 - 14
6 B - 2 B + 2 C - 2 C = 8
4 B = 8
1 B = 8 ÷ 4 = 2
(c)
Substitute 1 B = 2 into (3).
1 B + 1 C = 7
2 + 1 C = 7
1 C = 7 - 2 = 5
Answer(s): (a) 7; (b) 2; (c) 5