SOLUTION: The difference between two numbers is 9. Six times the larger number is 15 times the smaller number. Write a system of equations describing the given conditions. Then solve the sys

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Question 625283: The difference between two numbers is 9. Six times the larger number is 15 times the smaller number. Write a system of equations describing the given conditions. Then solve the system by the substitution method and find the two numbers.
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x be the larger and y be the smaller number

The difference between two numbers is 9
x-y=9
x=9+y...........(1)
Six times the larger number is 15 times the smaller number
6x=15y..........(2)
Substitute the value of x from (1) to (2)
6(9+y)=15y..........(2)
54+6y=15y
6y-15y=-54
-9y=-54
Divide by -9 both sides of the above equation
-9y/-9=-54/-9
y=6
Put the value of y in (1)
x=9+y
x=9+6
x=15
Numbers are 15 and 6