4 M + 2 N = 24
5 M + 3 N = 31
Fill in the blanks.
- 1 M + 1 N = _____
- 1 M = _____
- 1 N = _____
(a)
4 M + 2 N = 24 --- (1)
5 M + 3 N = 31 --- (2)
(2) - (1)
(5 M + 3 N) - (4 M + 2 N) = 31 - 24
5 M - 4 M + 3 N - 2 N = 7
1 M + 1 N = 7 --- (3)
1 M + 1 N = 7
(b)
Make N the same.
LCM of 1 and 2 = 2
(3) x 2
2 M + 2 N = 14 --- (4)
(1) - (4)
(4 M + 2 N) - (2 M + 2 N) = 24 - 14
4 M - 2 M + 2 N - 2 N = 10
2 M = 10
1 M = 10 ÷ 2 = 5
(c)
Substitute 1 M = 5 into (3).
1 M + 1 N = 7
5 + 1 N = 7
1 N = 7 - 5 = 2
Answer(s): (a) 7; (b) 5; (c) 2
