5 A + 2 B = 24
6 A + 3 B = 30
Fill in the blanks.
- 1 A + 1 B = _____
- 1 A = _____
- 1 B = _____
(a)
5 A + 2 B = 24 --- (1)
6 A + 3 B = 30 --- (2)
(2) - (1)
(6 A + 3 B) - (5 A + 2 B) = 30 - 24
6 A - 5 A + 3 B - 2 B = 6
1 A + 1 B = 6 --- (3)
1 A + 1 B = 6
(b)
Make B the same.
LCM of 1 and 2 = 2
(3) x 2
2 A + 2 B = 12 --- (4)
(1) - (4)
(5 A + 2 B) - (2 A + 2 B) = 24 - 12
5 A - 2 A + 2 B - 2 B = 12
3 A = 12
1 A = 12 ÷ 3 = 4
(c)
Substitute 1 A = 4 into (3).
1 A + 1 B = 6
4 + 1 B = 6
1 B = 6 - 4 = 2
Answer(s): (a) 6; (b) 4; (c) 2