6 S + 3 T = 33
7 S + 4 T = 41
Fill in the blanks.
- 1 S + 1 T = _____
- 1 S = _____
- 1 T = _____
(a)
6 S + 3 T = 33 --- (1)
7 S + 4 T = 41 --- (2)
(2) - (1)
(7 S + 4 T) - (6 S + 3 T) = 41 - 33
7 S - 6 S + 4 T - 3 T = 8
1 S + 1 T = 8 --- (3)
1 S + 1 T = 8
(b)
Make T the same.
LCM of 1 and 3 = 3
(3) x 3
3 S + 3 T = 24 --- (4)
(1) - (4)
(6 S + 3 T) - (3 S + 3 T) = 33 - 24
6 S - 3 S + 3 T - 3 T = 9
3 S = 9
1 S = 9 ÷ 3 = 3
(c)
Substitute 1 S = 3 into (3).
1 S + 1 T = 8
3 + 1 T = 8
1 T = 8 - 3 = 5
Answer(s): (a) 8; (b) 3; (c) 5