First, let's create two variables to express the girls' ages.
x=age of girl 1
y = age of girl 2
Now, let's create our expressions
x+y = 24
x-y=6
Let's solve by elimination
2x = 30
Divide both sides by 2
x=15
We can plug 15 in for x into one of our expressions
15 + y = 24
Subtract both sides by 15
y = 9
The older girl is 15 years old and the younger girl is 9 years old.