4 X + 2 Y = 26
5 X + 3 Y = 34
Fill in the blanks.
- 1 X + 1 Y = _____
- 1 X = _____
- 1 Y = _____
(a)
4 X + 2 Y = 26 --- (1)
5 X + 3 Y = 34 --- (2)
(2) - (1)
(5 X + 3 Y) - (4 X + 2 Y) = 34 - 26
5 X - 4 X + 3 Y - 2 Y = 8
1 X + 1 Y = 8 --- (3)
1 X + 1 Y = 8
(b)
Make Y the same.
LCM of 1 and 2 = 2
(3) x 2
2 X + 2 Y = 16 --- (4)
(1) - (4)
(4 X + 2 Y) - (2 X + 2 Y) = 26 - 16
4 X - 2 X + 2 Y - 2 Y = 10
2 X = 10
1 X = 10 ÷ 2 = 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