A child can be left home alone for small amounts of time when they are ages 9 to 12 years old.
However you must also determine the child's maturity and determine if they are safely able to stay alone at home while you're away at work or doing short errands.
Never leave a child home along for an entire day until they are at least 15 years old.
However I remember that when I was 13 years old my parents had to go out of state to see family for a family reunion and I did not want to go.
I also did not want a babysitter and so I begged and pleaded with my parents to let me stay home alone while they were away for the week.
Finally my parents decided that it would be okay and I knew how to cook, could go to the store down the street and buy some food, take care of the house etc.
I was perfectly fine and my parents just had a trusted neighbor come over to check on me and make sure I was okay.
However you can't leave every 13 year old home alone for that long because some 13 year olds cannot be trusted.
And your state may have laws on when you can leave a child home alone legally so check with your state to be sure.
Some children 13 years and older, who are at an adequate level of maturity, may be left alone and may perform the role of babysitters depending on the maturity.