6 K + 3 L = 39
7 K + 4 L = 47
Fill in the blanks.
- 1 K + 1 L = _____
- 1 K = _____
- 1 L = _____
(a)
6 K + 3 L = 39 --- (1)
7 K + 4 L = 47 --- (2)
(2) - (1)
(7 K + 4 L) - (6 K + 3 L) = 47 - 39
7 K - 6 K + 4 L - 3 L = 8
1 K + 1 L = 8 --- (3)
1 K + 1 L = 8
(b)
Make L the same.
LCM of 1 and 3 = 3
(3) x 3
3 K + 3 L = 24 --- (4)
(1) - (4)
(6 K + 3 L) - (3 K + 3 L) = 39 - 24
6 K - 3 K + 3 L - 3 L = 15
3 K = 15
1 K = 15 ÷ 3 = 5
(c)
Substitute 1 K = 5 into (3).
1 K + 1 L = 8
5 + 1 L = 8
1 L = 8 - 5 = 3
Answer(s): (a) 8; (b) 5; (c) 3