6 X + 2 Y = 18
7 X + 3 Y = 23
Fill in the blanks.
- 1 X + 1 Y = _____
- 1 X = _____
- 1 Y = _____
(a)
6 X + 2 Y = 18 --- (1)
7 X + 3 Y = 23 --- (2)
(2) - (1)
(7 X + 3 Y) - (6 X + 2 Y) = 23 - 18
7 X - 6 X + 3 Y - 2 Y = 5
1 X + 1 Y = 5 --- (3)
1 X + 1 Y = 5
(b)
Make Y the same.
LCM of 1 and 2 = 2
(3) x 2
2 X + 2 Y = 10 --- (4)
(1) - (4)
(6 X + 2 Y) - (2 X + 2 Y) = 18 - 10
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 = 5
2 + 1 Y = 5
1 Y = 5 - 2 = 3
Answer(s): (a) 5; (b) 2; (c) 3