Alexander Adams was born 1776 and married Isabelle Miller. He could have married again but if Elizabeth born 1809 there would be a vast age difference. Not impossible but unlikely
This is one where I have two totally different wives for John Adams, son of Matthew and I am confused. One source that has proved reliable shows him married to Rhoda Martin who is a widow in the 1850 Searcy County census. However James Tims who is apparently a descendant of John says he married Elizabeth Cayce and they are in Izard County. This clearly needs more research. Contact me privately and I will give you James E-Mail address. Please let me know if you are able to clear up this puzzle. I would like to set my records straight.