5 S + 3 T = 27
6 S + 4 T = 34
Fill in the blanks.
- 1 S + 1 T = _____
- 1 S = _____
- 1 T = _____
(a)
5 S + 3 T = 27 --- (1)
6 S + 4 T = 34 --- (2)
(2) - (1)
(6 S + 4 T) - (5 S + 3 T) = 34 - 27
6 S - 5 S + 4 T - 3 T = 7
1 S + 1 T = 7 --- (3)
1 S + 1 T = 7
(b)
Make T the same.
LCM of 1 and 3 = 3
(3) x 3
3 S + 3 T = 21 --- (4)
(1) - (4)
(5 S + 3 T) - (3 S + 3 T) = 27 - 21
5 S - 3 S + 3 T - 3 T = 6
2 S = 6
1 S = 6 ÷ 2 = 3
(c)
Substitute 1 S = 3 into (3).
1 S + 1 T = 7
3 + 1 T = 7
1 T = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4
