6 E + 2 F = 34
7 E + 3 F = 41
Fill in the blanks.
- 1 E + 1 F = _____
- 1 E = _____
- 1 F = _____
(a)
6 E + 2 F = 34 --- (1)
7 E + 3 F = 41 --- (2)
(2) - (1)
(7 E + 3 F) - (6 E + 2 F) = 41 - 34
7 E - 6 E + 3 F - 2 F = 7
1 E + 1 F = 7 --- (3)
1 E + 1 F = 7
(b)
Make F the same.
LCM of 1 and 2 = 2
(3) x 2
2 E + 2 F = 14 --- (4)
(1) - (4)
(6 E + 2 F) - (2 E + 2 F) = 34 - 14
6 E - 2 E + 2 F - 2 F = 20
4 E = 20
1 E = 20 ÷ 4 = 5
(c)
Substitute 1 E = 5 into (3).
1 E + 1 F = 7
5 + 1 F = 7
1 F = 7 - 5 = 2
Answer(s): (a) 7; (b) 5; (c) 2