4 S + 2 T = 26
5 S + 3 T = 35
Fill in the blanks.
- 1 S + 1 T = _____
- 1 S = _____
- 1 T = _____
(a)
4 S + 2 T = 26 --- (1)
5 S + 3 T = 35 --- (2)
(2) - (1)
(5 S + 3 T) - (4 S + 2 T) = 35 - 26
5 S - 4 S + 3 T - 2 T = 9
1 S + 1 T = 9 --- (3)
1 S + 1 T = 9
(b)
Make T the same.
LCM of 1 and 2 = 2
(3) x 2
2 S + 2 T = 18 --- (4)
(1) - (4)
(4 S + 2 T) - (2 S + 2 T) = 26 - 18
4 S - 2 S + 2 T - 2 T = 8
2 S = 8
1 S = 8 ÷ 2 = 4
(c)
Substitute 1 S = 4 into (3).
1 S + 1 T = 9
4 + 1 T = 9
1 T = 9 - 4 = 5
Answer(s): (a) 9; (b) 4; (c) 5