6 D + 4 E = 24
7 D + 5 E = 29
Fill in the blanks.
- 1 D + 1 E = _____
- 1 D = _____
- 1 E = _____
(a)
6 D + 4 E = 24 --- (1)
7 D + 5 E = 29 --- (2)
(2) - (1)
(7 D + 5 E) - (6 D + 4 E) = 29 - 24
7 D - 6 D + 5 E - 4 E = 5
1 D + 1 E = 5 --- (3)
1 D + 1 E = 5
(b)
Make E the same.
LCM of 1 and 4 = 4
(3) x 4
4 D + 4 E = 20 --- (4)
(1) - (4)
(6 D + 4 E) - (4 D + 4 E) = 24 - 20
6 D - 4 D + 4 E - 4 E = 4
2 D = 4
1 D = 4 ÷ 2 = 2
(c)
Substitute 1 D = 2 into (3).
1 D + 1 E = 5
2 + 1 E = 5
1 E = 5 - 2 = 3
Answer(s): (a) 5; (b) 2; (c) 3