5 U + 2 V = 19
6 U + 3 V = 24
Fill in the blanks.
- 1 U + 1 V = _____
- 1 U = _____
- 1 V = _____
(a)
5 U + 2 V = 19 --- (1)
6 U + 3 V = 24 --- (2)
(2) - (1)
(6 U + 3 V) - (5 U + 2 V) = 24 - 19
6 U - 5 U + 3 V - 2 V = 5
1 U + 1 V = 5 --- (3)
1 U + 1 V = 5
(b)
Make V the same.
LCM of 1 and 2 = 2
(3) x 2
2 U + 2 V = 10 --- (4)
(1) - (4)
(5 U + 2 V) - (2 U + 2 V) = 19 - 10
5 U - 2 U + 2 V - 2 V = 9
3 U = 9
1 U = 9 ÷ 3 = 3
(c)
Substitute 1 U = 3 into (3).
1 U + 1 V = 5
3 + 1 V = 5
1 V = 5 - 3 = 2
Answer(s): (a) 5; (b) 3; (c) 2