Two Simple Equations

You have apples and peaches. All together there are 12 fruits. There are two more apples than peaches. How many of each fruit are there? Note that similar problems do not always have a solution. Try to think of when they do and when they do not.

(You may notice that the problem of the total of, say, 12 fruits, in which there are 3 more apples than peaches has no solution. One reason is that due to the counting nature of the problem we are looking for an integer solutions. But there could not be two whole numbers whose sum is even, while the difference is odd. For additional brooding, see the page on Math reform and thoughts of where mathematics starts.)