One way to look at it is as follows:
Each of the addends (numbers being added together) in the second sum are one less than one of the addends in the first sum: 6 is one less than 7, and 1 is one less than 2. So the second sum should be a total of two less than the first sum. If you know 2+7 is 9, then the second sum should be two less than that: 7.
Of course, if you can analyze the problem this way you can probably also add 6+1 directly. I find that the technique can come in handy when dealing with larger numbers. For example, I know that 4x25 = 100 - thinking about four quarters in a dollar can make this calculation easy. From this, I can also easily do 4x24 - since each 24 is one less than 25, if I add four of them together, I should get 4 less than 4x25. Thus I can quickly find that 4x24=100-4=96.