6 Y + 4 Z = 68
7 Y + 5 Z = 81
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 2 Y + 5 Z = _____
(a)
6 Y + 4 Z = 68 --- (1)
7 Y + 5 Z = 81 --- (2)
Make Z the same.
LCM of 4 and 5 = 20
(1) x 5
30 Y + 20 Z = 340 --- (3)
(2) x 4
28 Y + 20 Z = 324 --- (4)
(a)
(3) - (4)
(30 Y + 20 Z) - (28 Y + 20 Z) = 340 - 324
30 Y - 28 Y + 20 Z - 20 Z = 16
2 Y = 16
1 Y = 16 ÷ 2 = 8
(b)
Substitute Y = 8 into (1).
6 Y + 4 Z = 68
6 x 8 + 4 Z = 68
48 + 4 Z = 68
4 Z = 68 - 48 = 20
1 Z = 20 ÷ 4 = 5
(c)
2 Y + 5 Z
= 2 x 8 + 5 x 5
= 16 + 25
= 41
Answer(s): (a) 8; (b) 5; (c) 41