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