6 L + 3 M = 33
7 L + 4 M = 40
Fill in the blanks.
- 1 L + 1 M = _____
- 1 L = _____
- 1 M = _____
(a)
6 L + 3 M = 33 --- (1)
7 L + 4 M = 40 --- (2)
(2) - (1)
(7 L + 4 M) - (6 L + 3 M) = 40 - 33
7 L - 6 L + 4 M - 3 M = 7
1 L + 1 M = 7 --- (3)
1 L + 1 M = 7
(b)
Make M the same.
LCM of 1 and 3 = 3
(3) x 3
3 L + 3 M = 21 --- (4)
(1) - (4)
(6 L + 3 M) - (3 L + 3 M) = 33 - 21
6 L - 3 L + 3 M - 3 M = 12
3 L = 12
1 L = 12 ÷ 3 = 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