SOLUTION: The difference of two numbers is 7. Their sum is 13 a) define the varable b) state the system of equations that model this situation c) determine the numbers

Question 1011833: The difference of two numbers is 7. Their sum is 13
a) define the varable
b) state the system of equations that model this situation
c) determine the numbers
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
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.

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