6 P + 4 Q = 38
7 P + 5 Q = 46
Fill in the blanks.
- 1 P + 1 Q = _____
- 1 P = _____
- 1 Q = _____
(a)
6 P + 4 Q = 38 --- (1)
7 P + 5 Q = 46 --- (2)
(2) - (1)
(7 P + 5 Q) - (6 P + 4 Q) = 46 - 38
7 P - 6 P + 5 Q - 4 Q = 8
1 P + 1 Q = 8 --- (3)
1 P + 1 Q = 8
(b)
Make Q the same.
LCM of 1 and 4 = 4
(3) x 4
4 P + 4 Q = 32 --- (4)
(1) - (4)
(6 P + 4 Q) - (4 P + 4 Q) = 38 - 32
6 P - 4 P + 4 Q - 4 Q = 6
2 P = 6
1 P = 6 ÷ 2 = 3
(c)
Substitute 1 P = 3 into (3).
1 P + 1 Q = 8
3 + 1 Q = 8
1 Q = 8 - 3 = 5
Answer(s): (a) 8; (b) 3; (c) 5
