6 Y + 4 Z = 26
7 Y + 5 Z = 31
Fill in the blanks.
- 1 Y + 1 Z = _____
- 1 Y = _____
- 1 Z = _____
(a)
6 Y + 4 Z = 26 --- (1)
7 Y + 5 Z = 31 --- (2)
(2) - (1)
(7 Y + 5 Z) - (6 Y + 4 Z) = 31 - 26
7 Y - 6 Y + 5 Z - 4 Z = 5
1 Y + 1 Z = 5 --- (3)
1 Y + 1 Z = 5
(b)
Make Z the same.
LCM of 1 and 4 = 4
(3) x 4
4 Y + 4 Z = 20 --- (4)
(1) - (4)
(6 Y + 4 Z) - (4 Y + 4 Z) = 26 - 20
6 Y - 4 Y + 4 Z - 4 Z = 6
2 Y = 6
1 Y = 6 ÷ 2 = 3
(c)
Substitute 1 Y = 3 into (3).
1 Y + 1 Z = 5
3 + 1 Z = 5
1 Z = 5 - 3 = 2
Answer(s): (a) 5; (b) 3; (c) 2