6 U + 4 V = 34
7 U + 5 V = 41
Fill in the blanks.
- 1 U + 1 V = _____
- 1 U = _____
- 1 V = _____
(a)
6 U + 4 V = 34 --- (1)
7 U + 5 V = 41 --- (2)
(2) - (1)
(7 U + 5 V) - (6 U + 4 V) = 41 - 34
7 U - 6 U + 5 V - 4 V = 7
1 U + 1 V = 7 --- (3)
1 U + 1 V = 7
(b)
Make V the same.
LCM of 1 and 4 = 4
(3) x 4
4 U + 4 V = 28 --- (4)
(1) - (4)
(6 U + 4 V) - (4 U + 4 V) = 34 - 28
6 U - 4 U + 4 V - 4 V = 6
2 U = 6
1 U = 6 ÷ 2 = 3
(c)
Substitute 1 U = 3 into (3).
1 U + 1 V = 7
3 + 1 V = 7
1 V = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4
