The difference of two numbers is 7. Their sum is 13
a) define the variables 

b) state the system of equations that's model this situation 

c) define the numbers
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Let x = the greater number, y = the smaller number.

The system is

x - y = 7   (1)
x + y = 13  (2)

To solve it, add the equations (1) and (2) (both the left sides and the right sides). You will get

2x = 20. Hence, x =  = 10.

Then from (1) y = x - 7 = 10 - 7 = 3.

Answer. The larger number is 10. The smaller number is 3.