6 L + 4 M = 34
7 L + 5 M = 41
Fill in the blanks.
- 1 L + 1 M = _____
- 1 L = _____
- 1 M = _____
(a)
6 L + 4 M = 34 --- (1)
7 L + 5 M = 41 --- (2)
(2) - (1)
(7 L + 5 M) - (6 L + 4 M) = 41 - 34
7 L - 6 L + 5 M - 4 M = 7
1 L + 1 M = 7 --- (3)
1 L + 1 M = 7
(b)
Make M the same.
LCM of 1 and 4 = 4
(3) x 4
4 L + 4 M = 28 --- (4)
(1) - (4)
(6 L + 4 M) - (4 L + 4 M) = 34 - 28
6 L - 4 L + 4 M - 4 M = 6
2 L = 6
1 L = 6 ÷ 2 = 3
(c)
Substitute 1 L = 3 into (3).
1 L + 1 M = 7
3 + 1 M = 7
1 M = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4