5 A + 3 B = 27
6 A + 4 B = 34
Fill in the blanks.
- 1 A + 1 B = _____
- 1 A = _____
- 1 B = _____
(a)
5 A + 3 B = 27 --- (1)
6 A + 4 B = 34 --- (2)
(2) - (1)
(6 A + 4 B) - (5 A + 3 B) = 34 - 27
6 A - 5 A + 4 B - 3 B = 7
1 A + 1 B = 7 --- (3)
1 A + 1 B = 7
(b)
Make B the same.
LCM of 1 and 3 = 3
(3) x 3
3 A + 3 B = 21 --- (4)
(1) - (4)
(5 A + 3 B) - (3 A + 3 B) = 27 - 21
5 A - 3 A + 3 B - 3 B = 6
2 A = 6
1 A = 6 ÷ 2 = 3
(c)
Substitute 1 A = 3 into (3).
1 A + 1 B = 7
3 + 1 B = 7
1 B = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4
