4 B + 2 C = 26
5 B + 3 C = 34
Fill in the blanks.
- 1 B + 1 C = _____
- 1 B = _____
- 1 C = _____
(a)
4 B + 2 C = 26 --- (1)
5 B + 3 C = 34 --- (2)
(2) - (1)
(5 B + 3 C) - (4 B + 2 C) = 34 - 26
5 B - 4 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)
(4 B + 2 C) - (2 B + 2 C) = 26 - 16
4 B - 2 B + 2 C - 2 C = 10
2 B = 10
1 B = 10 ÷ 2 = 5
(c)
Substitute 1 B = 5 into (3).
1 B + 1 C = 8
5 + 1 C = 8
1 C = 8 - 5 = 3
Answer(s): (a) 8; (b) 5; (c) 3