6 Y + 4 Z = 62
7 Y + 5 Z = 74
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 4 Y + 2 Z = _____
(a)
6 Y + 4 Z = 62 --- (1)
7 Y + 5 Z = 74 --- (2)
Make Z the same.
LCM of 4 and 5 = 20
(1) x 5
30 Y + 20 Z = 310 --- (3)
(2) x 4
28 Y + 20 Z = 296 --- (4)
(a)
(3) - (4)
(30 Y + 20 Z) - (28 Y + 20 Z) = 310 - 296
30 Y - 28 Y + 20 Z - 20 Z = 14
2 Y = 14
1 Y = 14 ÷ 2 = 7
(b)
Substitute Y = 7 into (1).
6 Y + 4 Z = 62
6 x 7 + 4 Z = 62
42 + 4 Z = 62
4 Z = 62 - 42 = 20
1 Z = 20 ÷ 4 = 5
(c)
4 Y + 2 Z
= 4 x 7 + 2 x 5
= 28 + 10
= 38
Answer(s): (a) 7; (b) 5; (c) 38
