8 Y + 6 Z = 60
9 Y + 7 Z = 69
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 4 Y + 5 Z = _____
(a)
8 Y + 6 Z = 60 --- (1)
9 Y + 7 Z = 69 --- (2)
Make Z the same.
LCM of 6 and 7 = 42
(1) x 7
56 Y + 42 Z = 420 --- (3)
(2) x 6
54 Y + 42 Z = 414 --- (4)
(a)
(3) - (4)
(56 Y + 42 Z) - (54 Y + 42 Z) = 420 - 414
56 Y - 54 Y + 42 Z - 42 Z = 6
2 Y = 6
1 Y = 6 ÷ 2 = 3
(b)
Substitute Y = 3 into (1).
8 Y + 6 Z = 60
8 x 3 + 6 Z = 60
24 + 6 Z = 60
6 Z = 60 - 24 = 36
1 Z = 36 ÷ 6 = 6
(c)
4 Y + 5 Z
= 4 x 3 + 5 x 6
= 12 + 30
= 42
Answer(s): (a) 3; (b) 6; (c) 42
