5 A + 2 B = 31
6 A + 3 B = 39
Fill in the blanks.
- 1 A + 1 B = _____
- 1 A = _____
- 1 B = _____
(a)
5 A + 2 B = 31 --- (1)
6 A + 3 B = 39 --- (2)
(2) - (1)
(6 A + 3 B) - (5 A + 2 B) = 39 - 31
6 A - 5 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)
(5 A + 2 B) - (2 A + 2 B) = 31 - 16
5 A - 2 A + 2 B - 2 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