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