7 S + 3 T = 26
8 S + 4 T = 32
Fill in the blanks.
- 1 S = _____
- 1 T = _____
- 5 S + 4 T = _____
(a)
7 S + 3 T = 26 --- (1)
8 S + 4 T = 32 --- (2)
Make T the same.
LCM of 3 and 4 = 12
(1) x 4
28 S + 12 T = 104 --- (3)
(2) x 3
24 S + 12 T = 96 --- (4)
(a)
(3) - (4)
(28 S + 12 T) - (24 S + 12 T) = 104 - 96
28 S - 24 S + 12 T - 12 T = 8
4 S = 8
1 S = 8 ÷ 4 = 2
(b)
Substitute S = 2 into (1).
7 S + 3 T = 26
7 x 2 + 3 T = 26
14 + 3 T = 26
3 T = 26 - 14 = 12
1 T = 12 ÷ 3 = 4
(c)
5 S + 4 T
= 5 x 2 + 4 x 4
= 10 + 16
= 26
Answer(s): (a) 2; (b) 4; (c) 26