For this case we have:
x: Represents the number of carrot boxes
y: Represents the number of boxes of potatoes
Initially we have:

If you sold 68 boxes of carrot we have:

If you sold 71 boxes of potatoes, we have:

The number of boxes I take home is given by:

ANswer:
7 boxes of carrots left
There are 9 boxes of potatoes left
A total of 16 boxes remain