4 K + 2 L = 26
5 K + 3 L = 35
Fill in the blanks.
- 1 K + 1 L = _____
- 1 K = _____
- 1 L = _____
(a)
4 K + 2 L = 26 --- (1)
5 K + 3 L = 35 --- (2)
(2) - (1)
(5 K + 3 L) - (4 K + 2 L) = 35 - 26
5 K - 4 K + 3 L - 2 L = 9
1 K + 1 L = 9 --- (3)
1 K + 1 L = 9
(b)
Make L the same.
LCM of 1 and 2 = 2
(3) x 2
2 K + 2 L = 18 --- (4)
(1) - (4)
(4 K + 2 L) - (2 K + 2 L) = 26 - 18
4 K - 2 K + 2 L - 2 L = 8
2 K = 8
1 K = 8 ÷ 2 = 4
(c)
Substitute 1 K = 4 into (3).
1 K + 1 L = 9
4 + 1 L = 9
1 L = 9 - 4 = 5
Answer(s): (a) 9; (b) 4; (c) 5