8 Y + 5 Z = 107
9 Y + 6 Z = 123
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 4 Y + 3 Z = _____
(a)
8 Y + 5 Z = 107 --- (1)
9 Y + 6 Z = 123 --- (2)
Make Z the same.
LCM of 5 and 6 = 30
(1) x 6
48 Y + 30 Z = 642 --- (3)
(2) x 5
45 Y + 30 Z = 615 --- (4)
(a)
(3) - (4)
(48 Y + 30 Z) - (45 Y + 30 Z) = 642 - 615
48 Y - 45 Y + 30 Z - 30 Z = 27
3 Y = 27
1 Y = 27 ÷ 3 = 9
(b)
Substitute Y = 9 into (1).
8 Y + 5 Z = 107
8 x 9 + 5 Z = 107
72 + 5 Z = 107
5 Z = 107 - 72 = 35
1 Z = 35 ÷ 5 = 7
(c)
4 Y + 3 Z
= 4 x 9 + 3 x 7
= 36 + 21
= 57
Answer(s): (a) 9; (b) 7; (c) 57
