Problem: The difference of two numbers is 5.
The difference of two numbers is 5. 4 times the larger number is 6 times the smaller number. What are the numbers?
1) x - y = 5
2) 4x = 6y
4x - 6y = 0
6(x - y) = 5 * 6
3) 6x - 6y = 30
6x - 6y = 30
-(4x - 6y = 0) Subtract equation 2 from equation 3
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2x = 30
2x = 30
x = 15
x - y = 5 equation 1
15 - y = 5
15 - y - 5 = 5 - 5
10 - y = 0
10 - y + y = 0 + y
10 = y
Check it.
4x = 6y equation 2
4(15) = 6(10)
60 = 60
Answer: x = 15, y = 10