6 G + 2 H = 22
7 G + 3 H = 29
Fill in the blanks.
- 1 G + 1 H = _____
- 1 G = _____
- 1 H = _____
(a)
6 G + 2 H = 22 --- (1)
7 G + 3 H = 29 --- (2)
(2) - (1)
(7 G + 3 H) - (6 G + 2 H) = 29 - 22
7 G - 6 G + 3 H - 2 H = 7
1 G + 1 H = 7 --- (3)
1 G + 1 H = 7
(b)
Make H the same.
LCM of 1 and 2 = 2
(3) x 2
2 G + 2 H = 14 --- (4)
(1) - (4)
(6 G + 2 H) - (2 G + 2 H) = 22 - 14
6 G - 2 G + 2 H - 2 H = 8
4 G = 8
1 G = 8 ÷ 4 = 2
(c)
Substitute 1 G = 2 into (3).
1 G + 1 H = 7
2 + 1 H = 7
1 H = 7 - 2 = 5
Answer(s): (a) 7; (b) 2; (c) 5
