6 X + 3 Y = 27
7 X + 4 Y = 34
Fill in the blanks.
- 1 X + 1 Y = _____
- 1 X = _____
- 1 Y = _____
(a)
6 X + 3 Y = 27 --- (1)
7 X + 4 Y = 34 --- (2)
(2) - (1)
(7 X + 4 Y) - (6 X + 3 Y) = 34 - 27
7 X - 6 X + 4 Y - 3 Y = 7
1 X + 1 Y = 7 --- (3)
1 X + 1 Y = 7
(b)
Make Y the same.
LCM of 1 and 3 = 3
(3) x 3
3 X + 3 Y = 21 --- (4)
(1) - (4)
(6 X + 3 Y) - (3 X + 3 Y) = 27 - 21
6 X - 3 X + 3 Y - 3 Y = 6
3 X = 6
1 X = 6 ÷ 3 = 2
(c)
Substitute 1 X = 2 into (3).
1 X + 1 Y = 7
2 + 1 Y = 7
1 Y = 7 - 2 = 5
Answer(s): (a) 7; (b) 2; (c) 5