SOLUTION: 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

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
------------------------------------------------------------

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.