6 S + 2 T = 36
7 S + 3 T = 44
Fill in the blanks.
- 1 S + 1 T = _____
- 1 S = _____
- 1 T = _____
(a)
6 S + 2 T = 36 --- (1)
7 S + 3 T = 44 --- (2)
(2) - (1)
(7 S + 3 T) - (6 S + 2 T) = 44 - 36
7 S - 6 S + 3 T - 2 T = 8
1 S + 1 T = 8 --- (3)
1 S + 1 T = 8
(b)
Make T the same.
LCM of 1 and 2 = 2
(3) x 2
2 S + 2 T = 16 --- (4)
(1) - (4)
(6 S + 2 T) - (2 S + 2 T) = 36 - 16
6 S - 2 S + 2 T - 2 T = 20
4 S = 20
1 S = 20 ÷ 4 = 5
(c)
Substitute 1 S = 5 into (3).
1 S + 1 T = 8
5 + 1 T = 8
1 T = 8 - 5 = 3
Answer(s): (a) 8; (b) 5; (c) 3