4 F + 2 G = 26
5 F + 3 G = 35
Fill in the blanks.
- 1 F + 1 G = _____
- 1 F = _____
- 1 G = _____
(a)
4 F + 2 G = 26 --- (1)
5 F + 3 G = 35 --- (2)
(2) - (1)
(5 F + 3 G) - (4 F + 2 G) = 35 - 26
5 F - 4 F + 3 G - 2 G = 9
1 F + 1 G = 9 --- (3)
1 F + 1 G = 9
(b)
Make G the same.
LCM of 1 and 2 = 2
(3) x 2
2 F + 2 G = 18 --- (4)
(1) - (4)
(4 F + 2 G) - (2 F + 2 G) = 26 - 18
4 F - 2 F + 2 G - 2 G = 8
2 F = 8
1 F = 8 ÷ 2 = 4
(c)
Substitute 1 F = 4 into (3).
1 F + 1 G = 9
4 + 1 G = 9
1 G = 9 - 4 = 5
Answer(s): (a) 9; (b) 4; (c) 5
