6 M + 2 N = 22
7 M + 3 N = 27
Fill in the blanks.
- 1 M + 1 N = _____
- 1 M = _____
- 1 N = _____
(a)
6 M + 2 N = 22 --- (1)
7 M + 3 N = 27 --- (2)
(2) - (1)
(7 M + 3 N) - (6 M + 2 N) = 27 - 22
7 M - 6 M + 3 N - 2 N = 5
1 M + 1 N = 5 --- (3)
1 M + 1 N = 5
(b)
Make N the same.
LCM of 1 and 2 = 2
(3) x 2
2 M + 2 N = 10 --- (4)
(1) - (4)
(6 M + 2 N) - (2 M + 2 N) = 22 - 10
6 M - 2 M + 2 N - 2 N = 12
4 M = 12
1 M = 12 ÷ 4 = 3
(c)
Substitute 1 M = 3 into (3).
1 M + 1 N = 5
3 + 1 N = 5
1 N = 5 - 3 = 2
Answer(s): (a) 5; (b) 3; (c) 2