6 A + 3 B = 39
7 A + 4 B = 47
Fill in the blanks.
- 1 A + 1 B = _____
- 1 A = _____
- 1 B = _____
(a)
6 A + 3 B = 39 --- (1)
7 A + 4 B = 47 --- (2)
(2) - (1)
(7 A + 4 B) - (6 A + 3 B) = 47 - 39
7 A - 6 A + 4 B - 3 B = 8
1 A + 1 B = 8 --- (3)
1 A + 1 B = 8
(b)
Make B the same.
LCM of 1 and 3 = 3
(3) x 3
3 A + 3 B = 24 --- (4)
(1) - (4)
(6 A + 3 B) - (3 A + 3 B) = 39 - 24
6 A - 3 A + 3 B - 3 B = 15
3 A = 15
1 A = 15 ÷ 3 = 5
(c)
Substitute 1 A = 5 into (3).
1 A + 1 B = 8
5 + 1 B = 8
1 B = 8 - 5 = 3
Answer(s): (a) 8; (b) 5; (c) 3