4 F + 2 G = 24
5 F + 3 G = 31
Fill in the blanks.
- 1 F + 1 G = _____
- 1 F = _____
- 1 G = _____
(a)
4 F + 2 G = 24 --- (1)
5 F + 3 G = 31 --- (2)
(2) - (1)
(5 F + 3 G) - (4 F + 2 G) = 31 - 24
5 F - 4 F + 3 G - 2 G = 7
1 F + 1 G = 7 --- (3)
1 F + 1 G = 7
(b)
Make G the same.
LCM of 1 and 2 = 2
(3) x 2
2 F + 2 G = 14 --- (4)
(1) - (4)
(4 F + 2 G) - (2 F + 2 G) = 24 - 14
4 F - 2 F + 2 G - 2 G = 10
2 F = 10
1 F = 10 ÷ 2 = 5
(c)
Substitute 1 F = 5 into (3).
1 F + 1 G = 7
5 + 1 G = 7
1 G = 7 - 5 = 2
Answer(s): (a) 7; (b) 5; (c) 2