6 Y + 3 Z = 54
7 Y + 4 Z = 64
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 5 Y + 2 Z = _____
(a)
6 Y + 3 Z = 54 --- (1)
7 Y + 4 Z = 64 --- (2)
Make Z the same.
LCM of 3 and 4 = 12
(1) x 4
24 Y + 12 Z = 216 --- (3)
(2) x 3
21 Y + 12 Z = 192 --- (4)
(a)
(3) - (4)
(24 Y + 12 Z) - (21 Y + 12 Z) = 216 - 192
24 Y - 21 Y + 12 Z - 12 Z = 24
3 Y = 24
1 Y = 24 ÷ 3 = 8
(b)
Substitute Y = 8 into (1).
6 Y + 3 Z = 54
6 x 8 + 3 Z = 54
48 + 3 Z = 54
3 Z = 54 - 48 = 6
1 Z = 6 ÷ 3 = 2
(c)
5 Y + 2 Z
= 5 x 8 + 2 x 2
= 40 + 4
= 44
Answer(s): (a) 8; (b) 2; (c) 44