6 X + 2 Y = 22
7 X + 3 Y = 29
Fill in the blanks.
- 1 X + 1 Y = _____
- 1 X = _____
- 1 Y = _____
(a)
6 X + 2 Y = 22 --- (1)
7 X + 3 Y = 29 --- (2)
(2) - (1)
(7 X + 3 Y) - (6 X + 2 Y) = 29 - 22
7 X - 6 X + 3 Y - 2 Y = 7
1 X + 1 Y = 7 --- (3)
1 X + 1 Y = 7
(b)
Make Y the same.
LCM of 1 and 2 = 2
(3) x 2
2 X + 2 Y = 14 --- (4)
(1) - (4)
(6 X + 2 Y) - (2 X + 2 Y) = 22 - 14
6 X - 2 X + 2 Y - 2 Y = 8
4 X = 8
1 X = 8 ÷ 4 = 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