5 D + 3 E = 31
6 D + 4 E = 38
Fill in the blanks.
- 1 D + 1 E = _____
- 1 D = _____
- 1 E = _____
(a)
5 D + 3 E = 31 --- (1)
6 D + 4 E = 38 --- (2)
(2) - (1)
(6 D + 4 E) - (5 D + 3 E) = 38 - 31
6 D - 5 D + 4 E - 3 E = 7
1 D + 1 E = 7 --- (3)
1 D + 1 E = 7
(b)
Make E the same.
LCM of 1 and 3 = 3
(3) x 3
3 D + 3 E = 21 --- (4)
(1) - (4)
(5 D + 3 E) - (3 D + 3 E) = 31 - 21
5 D - 3 D + 3 E - 3 E = 10
2 D = 10
1 D = 10 ÷ 2 = 5
(c)
Substitute 1 D = 5 into (3).
1 D + 1 E = 7
5 + 1 E = 7
1 E = 7 - 5 = 2
Answer(s): (a) 7; (b) 5; (c) 2