5 A + 2 B = 19
6 A + 3 B = 24
Fill in the blanks.
- 1 A + 1 B = _____
- 1 A = _____
- 1 B = _____
(a)
5 A + 2 B = 19 --- (1)
6 A + 3 B = 24 --- (2)
(2) - (1)
(6 A + 3 B) - (5 A + 2 B) = 24 - 19
6 A - 5 A + 3 B - 2 B = 5
1 A + 1 B = 5 --- (3)
1 A + 1 B = 5
(b)
Make B the same.
LCM of 1 and 2 = 2
(3) x 2
2 A + 2 B = 10 --- (4)
(1) - (4)
(5 A + 2 B) - (2 A + 2 B) = 19 - 10
5 A - 2 A + 2 B - 2 B = 9
3 A = 9
1 A = 9 ÷ 3 = 3
(c)
Substitute 1 A = 3 into (3).
1 A + 1 B = 5
3 + 1 B = 5
1 B = 5 - 3 = 2
Answer(s): (a) 5; (b) 3; (c) 2