6 M + 4 N = 38
7 M + 5 N = 46
Fill in the blanks.
- 1 M + 1 N = _____
- 1 M = _____
- 1 N = _____
(a)
6 M + 4 N = 38 --- (1)
7 M + 5 N = 46 --- (2)
(2) - (1)
(7 M + 5 N) - (6 M + 4 N) = 46 - 38
7 M - 6 M + 5 N - 4 N = 8
1 M + 1 N = 8 --- (3)
1 M + 1 N = 8
(b)
Make N the same.
LCM of 1 and 4 = 4
(3) x 4
4 M + 4 N = 32 --- (4)
(1) - (4)
(6 M + 4 N) - (4 M + 4 N) = 38 - 32
6 M - 4 M + 4 N - 4 N = 6
2 M = 6
1 M = 6 ÷ 2 = 3
(c)
Substitute 1 M = 3 into (3).
1 M + 1 N = 8
3 + 1 N = 8
1 N = 8 - 3 = 5
Answer(s): (a) 8; (b) 3; (c) 5