The sum of two numbers is 35. The larger number is 13 more than the smaller number. What are the numbers?

Let b>a

b=a+13

a+b=35, using b found above we have:

a+a+13=35

2a+13=35

2a=22

a=11, and since b=a+13

b=24

So the two numbers are 11 and 24

Since a+b = 35

and a+13 = b

you can substitute (a+13) in for b for the first equation

a + a + 13 = 35

2a + 13 = 35

2a = 22

a = 11

you can now substitute in 11 for a in to the second equation

11 + 13 = b

24 = b

the two numbers and the 11 and 24