5 M + 2 N = 16
6 M + 3 N = 21
Fill in the blanks.
- 1 M + 1 N = _____
- 1 M = _____
- 1 N = _____
(a)
5 M + 2 N = 16 --- (1)
6 M + 3 N = 21 --- (2)
(2) - (1)
(6 M + 3 N) - (5 M + 2 N) = 21 - 16
6 M - 5 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)
(5 M + 2 N) - (2 M + 2 N) = 16 - 10
5 M - 2 M + 2 N - 2 N = 6
3 M = 6
1 M = 6 ÷ 3 = 2
(c)
Substitute 1 M = 2 into (3).
1 M + 1 N = 5
2 + 1 N = 5
1 N = 5 - 2 = 3
Answer(s): (a) 5; (b) 2; (c) 3
