One number exceeds another number by 5. if the sum of the two numbers is 39, what is the smaller number

Your 2 equations are:

x-y = 5 (because one number exceeds the other by 5. Therefore the difference is 5)

x+y = 39 (The sum of the two numbers is 39)

Solve one of the equations for one variable. I'm going to solve x - y = 5 for x.

x - y = 5 --> x = 5 + y

Now substitute 5 + y into the second equation for x.

x+y = 39

(5+y) + y = 39

5 + 2y = 39

2y = 34

y = 17

Now, you can solve for x by plugging y into one of the equations:

x - y = 5

x - 17 = 5

x = 22

Therefore, the smaller number is 17.

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