4 X + 2 Y = 16
5 X + 3 Y = 21
Fill in the blanks.
- 1 X + 1 Y = _____
- 1 X = _____
- 1 Y = _____
(a)
4 X + 2 Y = 16 --- (1)
5 X + 3 Y = 21 --- (2)
(2) - (1)
(5 X + 3 Y) - (4 X + 2 Y) = 21 - 16
5 X - 4 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)
(4 X + 2 Y) - (2 X + 2 Y) = 16 - 10
4 X - 2 X + 2 Y - 2 Y = 6
2 X = 6
1 X = 6 ÷ 2 = 3
(c)
Substitute 1 X = 3 into (3).
1 X + 1 Y = 5
3 + 1 Y = 5
1 Y = 5 - 3 = 2
Answer(s): (a) 5; (b) 3; (c) 2
