SOLUTION: He is the question below. I need to define the variable for x and y, write the appropriate equations, and solve the equation by either substitution, addition, or graphically. THX!

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Question 19786: He is the question below. I need to define the variable for x and y, write the appropriate equations, and solve the equation by either substitution, addition, or graphically. THX!
- The difference of two numbers is nine more than the smaller number, and the sum of the two numbers is 54. Find the smaller number.
Answer by xcentaur(357) (Show Source):
You can put this solution on YOUR website!
let the larger number be x
let the smaller number be y

difference of two numbers means (x-y)
this difference is nine more than the smaller number
x-y=9+y
x-y-y=9
x-2y=9......[1]

the sum of the two numbers is 54
x+y=54.......[2]

take the two equations together,
x-2y=9
x+y=54
subtract equation [2] from [1]
x-2y-(x+y)=9-54
x-2y-x-y=-45
-3y=-45
3y=45
y=15

x+y=54
x=54-y=54-15=39

x=39,y=15

Hope this helps,
Prabhat