6 F + 2 G = 20
7 F + 3 G = 26
Fill in the blanks.
- 1 F + 1 G = _____
- 1 F = _____
- 1 G = _____
(a)
6 F + 2 G = 20 --- (1)
7 F + 3 G = 26 --- (2)
(2) - (1)
(7 F + 3 G) - (6 F + 2 G) = 26 - 20
7 F - 6 F + 3 G - 2 G = 6
1 F + 1 G = 6 --- (3)
1 F + 1 G = 6
(b)
Make G the same.
LCM of 1 and 2 = 2
(3) x 2
2 F + 2 G = 12 --- (4)
(1) - (4)
(6 F + 2 G) - (2 F + 2 G) = 20 - 12
6 F - 2 F + 2 G - 2 G = 8
4 F = 8
1 F = 8 ÷ 4 = 2
(c)
Substitute 1 F = 2 into (3).
1 F + 1 G = 6
2 + 1 G = 6
1 G = 6 - 2 = 4
Answer(s): (a) 6; (b) 2; (c) 4