6 Y + 4 Z = 42
7 Y + 5 Z = 50
Fill in the blanks.
- 1 Y + 1 Z = _____
- 1 Y = _____
- 1 Z = _____
(a)
6 Y + 4 Z = 42 --- (1)
7 Y + 5 Z = 50 --- (2)
(2) - (1)
(7 Y + 5 Z) - (6 Y + 4 Z) = 50 - 42
7 Y - 6 Y + 5 Z - 4 Z = 8
1 Y + 1 Z = 8 --- (3)
1 Y + 1 Z = 8
(b)
Make Z the same.
LCM of 1 and 4 = 4
(3) x 4
4 Y + 4 Z = 32 --- (4)
(1) - (4)
(6 Y + 4 Z) - (4 Y + 4 Z) = 42 - 32
6 Y - 4 Y + 4 Z - 4 Z = 10
2 Y = 10
1 Y = 10 ÷ 2 = 5
(c)
Substitute 1 Y = 5 into (3).
1 Y + 1 Z = 8
5 + 1 Z = 8
1 Z = 8 - 5 = 3
Answer(s): (a) 8; (b) 5; (c) 3
