6 X + 3 Y = 39
7 X + 4 Y = 47
Fill in the blanks.
- 1 X + 1 Y = _____
- 1 X = _____
- 1 Y = _____
(a)
6 X + 3 Y = 39 --- (1)
7 X + 4 Y = 47 --- (2)
(2) - (1)
(7 X + 4 Y) - (6 X + 3 Y) = 47 - 39
7 X - 6 X + 4 Y - 3 Y = 8
1 X + 1 Y = 8 --- (3)
1 X + 1 Y = 8
(b)
Make Y the same.
LCM of 1 and 3 = 3
(3) x 3
3 X + 3 Y = 24 --- (4)
(1) - (4)
(6 X + 3 Y) - (3 X + 3 Y) = 39 - 24
6 X - 3 X + 3 Y - 3 Y = 15
3 X = 15
1 X = 15 ÷ 3 = 5
(c)
Substitute 1 X = 5 into (3).
1 X + 1 Y = 8
5 + 1 Y = 8
1 Y = 8 - 5 = 3
Answer(s): (a) 8; (b) 5; (c) 3