6 Y + 4 Z = 32
7 Y + 5 Z = 39
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 3 Y + 4 Z = _____
(a)
6 Y + 4 Z = 32 --- (1)
7 Y + 5 Z = 39 --- (2)
Make Z the same.
LCM of 4 and 5 = 20
(1) x 5
30 Y + 20 Z = 160 --- (3)
(2) x 4
28 Y + 20 Z = 156 --- (4)
(a)
(3) - (4)
(30 Y + 20 Z) - (28 Y + 20 Z) = 160 - 156
30 Y - 28 Y + 20 Z - 20 Z = 4
2 Y = 4
1 Y = 4 ÷ 2 = 2
(b)
Substitute Y = 2 into (1).
6 Y + 4 Z = 32
6 x 2 + 4 Z = 32
12 + 4 Z = 32
4 Z = 32 - 12 = 20
1 Z = 20 ÷ 4 = 5
(c)
3 Y + 4 Z
= 3 x 2 + 4 x 5
= 6 + 20
= 26
Answer(s): (a) 2; (b) 5; (c) 26
