5 T + 3 U = 31
6 T + 4 U = 38
Fill in the blanks.
- 1 T + 1 U = _____
- 1 T = _____
- 1 U = _____
(a)
5 T + 3 U = 31 --- (1)
6 T + 4 U = 38 --- (2)
(2) - (1)
(6 T + 4 U) - (5 T + 3 U) = 38 - 31
6 T - 5 T + 4 U - 3 U = 7
1 T + 1 U = 7 --- (3)
1 T + 1 U = 7
(b)
Make U the same.
LCM of 1 and 3 = 3
(3) x 3
3 T + 3 U = 21 --- (4)
(1) - (4)
(5 T + 3 U) - (3 T + 3 U) = 31 - 21
5 T - 3 T + 3 U - 3 U = 10
2 T = 10
1 T = 10 ÷ 2 = 5
(c)
Substitute 1 T = 5 into (3).
1 T + 1 U = 7
5 + 1 U = 7
1 U = 7 - 5 = 2
Answer(s): (a) 7; (b) 5; (c) 2
