6 J + 2 K = 18
7 J + 3 K = 23
Fill in the blanks.
- 1 J + 1 K = _____
- 1 J = _____
- 1 K = _____
(a)
6 J + 2 K = 18 --- (1)
7 J + 3 K = 23 --- (2)
(2) - (1)
(7 J + 3 K) - (6 J + 2 K) = 23 - 18
7 J - 6 J + 3 K - 2 K = 5
1 J + 1 K = 5 --- (3)
1 J + 1 K = 5
(b)
Make K the same.
LCM of 1 and 2 = 2
(3) x 2
2 J + 2 K = 10 --- (4)
(1) - (4)
(6 J + 2 K) - (2 J + 2 K) = 18 - 10
6 J - 2 J + 2 K - 2 K = 8
4 J = 8
1 J = 8 ÷ 4 = 2
(c)
Substitute 1 J = 2 into (3).
1 J + 1 K = 5
2 + 1 K = 5
1 K = 5 - 2 = 3
Answer(s): (a) 5; (b) 2; (c) 3
