The sum of two numbers is 21. the larger number is 6 less than twice the smaller number. find the two numbers.

The sum of two numbers
 x + y = 21
x = smaller number
y = larger number

Larger Number = y = (2x -6)
Substitute  (2x - 6) for y
x + y = 21
x + (2x - 6) = 21
3x - 6 = 21
3x = 21 + 6
3x = 27
3x / 3 = 27 / 3
x =  9
Smaller number = x = 9
Find the larger number by inserting 9 into (2x - 6)
(2x - 6)
(2(9) - 6)
18 - 6
12

So 
x = 9
y =12

Check our answer by inserting x = 9 and y = 12 into  x + y = 21
x + y =21
9 + 12 = 21
21 = 21 
So since we have 21 = 21 we know our answer is correct.