6 R + 2 S = 34
7 R + 3 S = 41
Fill in the blanks.
- 1 R + 1 S = _____
- 1 R = _____
- 1 S = _____
(a)
6 R + 2 S = 34 --- (1)
7 R + 3 S = 41 --- (2)
(2) - (1)
(7 R + 3 S) - (6 R + 2 S) = 41 - 34
7 R - 6 R + 3 S - 2 S = 7
1 R + 1 S = 7 --- (3)
1 R + 1 S = 7
(b)
Make S the same.
LCM of 1 and 2 = 2
(3) x 2
2 R + 2 S = 14 --- (4)
(1) - (4)
(6 R + 2 S) - (2 R + 2 S) = 34 - 14
6 R - 2 R + 2 S - 2 S = 20
4 R = 20
1 R = 20 ÷ 4 = 5
(c)
Substitute 1 R = 5 into (3).
1 R + 1 S = 7
5 + 1 S = 7
1 S = 7 - 5 = 2
Answer(s): (a) 7; (b) 5; (c) 2