6 S + 3 T = 42
7 S + 4 T = 51
Fill in the blanks.
- 1 S + 1 T = _____
- 1 S = _____
- 1 T = _____
(a)
6 S + 3 T = 42 --- (1)
7 S + 4 T = 51 --- (2)
(2) - (1)
(7 S + 4 T) - (6 S + 3 T) = 51 - 42
7 S - 6 S + 4 T - 3 T = 9
1 S + 1 T = 9 --- (3)
1 S + 1 T = 9
(b)
Make T the same.
LCM of 1 and 3 = 3
(3) x 3
3 S + 3 T = 27 --- (4)
(1) - (4)
(6 S + 3 T) - (3 S + 3 T) = 42 - 27
6 S - 3 S + 3 T - 3 T = 15
3 S = 15
1 S = 15 ÷ 3 = 5
(c)
Substitute 1 S = 5 into (3).
1 S + 1 T = 9
5 + 1 T = 9
1 T = 9 - 5 = 4
Answer(s): (a) 9; (b) 5; (c) 4
