6 E + 4 F = 32
7 E + 5 F = 39
Fill in the blanks.
- 1 E + 1 F = _____
- 1 E = _____
- 1 F = _____
(a)
6 E + 4 F = 32 --- (1)
7 E + 5 F = 39 --- (2)
(2) - (1)
(7 E + 5 F) - (6 E + 4 F) = 39 - 32
7 E - 6 E + 5 F - 4 F = 7
1 E + 1 F = 7 --- (3)
1 E + 1 F = 7
(b)
Make F the same.
LCM of 1 and 4 = 4
(3) x 4
4 E + 4 F = 28 --- (4)
(1) - (4)
(6 E + 4 F) - (4 E + 4 F) = 32 - 28
6 E - 4 E + 4 F - 4 F = 4
2 E = 4
1 E = 4 ÷ 2 = 2
(c)
Substitute 1 E = 2 into (3).
1 E + 1 F = 7
2 + 1 F = 7
1 F = 7 - 2 = 5
Answer(s): (a) 7; (b) 2; (c) 5