4 V + 2 W = 18
5 V + 3 W = 25
Fill in the blanks.
- 1 V + 1 W = _____
- 1 V = _____
- 1 W = _____
(a)
4 V + 2 W = 18 --- (1)
5 V + 3 W = 25 --- (2)
(2) - (1)
(5 V + 3 W) - (4 V + 2 W) = 25 - 18
5 V - 4 V + 3 W - 2 W = 7
1 V + 1 W = 7 --- (3)
1 V + 1 W = 7
(b)
Make W the same.
LCM of 1 and 2 = 2
(3) x 2
2 V + 2 W = 14 --- (4)
(1) - (4)
(4 V + 2 W) - (2 V + 2 W) = 18 - 14
4 V - 2 V + 2 W - 2 W = 4
2 V = 4
1 V = 4 ÷ 2 = 2
(c)
Substitute 1 V = 2 into (3).
1 V + 1 W = 7
2 + 1 W = 7
1 W = 7 - 2 = 5
Answer(s): (a) 7; (b) 2; (c) 5