6 K + 4 L = 36
7 K + 5 L = 43
Fill in the blanks.
- 1 K + 1 L = _____
- 1 K = _____
- 1 L = _____
(a)
6 K + 4 L = 36 --- (1)
7 K + 5 L = 43 --- (2)
(2) - (1)
(7 K + 5 L) - (6 K + 4 L) = 43 - 36
7 K - 6 K + 5 L - 4 L = 7
1 K + 1 L = 7 --- (3)
1 K + 1 L = 7
(b)
Make L the same.
LCM of 1 and 4 = 4
(3) x 4
4 K + 4 L = 28 --- (4)
(1) - (4)
(6 K + 4 L) - (4 K + 4 L) = 36 - 28
6 K - 4 K + 4 L - 4 L = 8
2 K = 8
1 K = 8 ÷ 2 = 4
(c)
Substitute 1 K = 4 into (3).
1 K + 1 L = 7
4 + 1 L = 7
1 L = 7 - 4 = 3
Answer(s): (a) 7; (b) 4; (c) 3