4 L + 2 M = 22
5 L + 3 M = 29
Fill in the blanks.
- 1 L + 1 M = _____
- 1 L = _____
- 1 M = _____
(a)
4 L + 2 M = 22 --- (1)
5 L + 3 M = 29 --- (2)
(2) - (1)
(5 L + 3 M) - (4 L + 2 M) = 29 - 22
5 L - 4 L + 3 M - 2 M = 7
1 L + 1 M = 7 --- (3)
1 L + 1 M = 7
(b)
Make M the same.
LCM of 1 and 2 = 2
(3) x 2
2 L + 2 M = 14 --- (4)
(1) - (4)
(4 L + 2 M) - (2 L + 2 M) = 22 - 14
4 L - 2 L + 2 M - 2 M = 8
2 L = 8
1 L = 8 ÷ 2 = 4
(c)
Substitute 1 L = 4 into (3).
1 L + 1 M = 7
4 + 1 M = 7
1 M = 7 - 4 = 3
Answer(s): (a) 7; (b) 4; (c) 3