What is the common purpose of the Ninth and Tenth amendments?

These Amendments, the Ninth and Tenth Amendments are the 'essential keys' necessary for the operation of our Constitution, these are the mobility elements.

The Ninth Amendment creates individual rights inferior to the rights of the People such as the right and responsibility to establish justice and to provide for the general defense. It is here that 'free' is defined ethically, legally, as under the law we are allowed to do equally. Free doesn't mean another thing.

The Tenth Amendment does to the State and Federal systems what the Ninth Amendment does to the individual's rights creating an inferior State and Federal system insuring the right's and responsibility's of the people to persevere. It is here that unconstitutionality is created and constitutionality is mandated. These Amendment's authorities are the essence of our home.
As this category is The Bible/OT, I will assume you are asking for the 9&10 Commandments of God. Here they are from Scripture:

Exodus 20:16-17New International Version (NIV)

16 "You shall not give false testimony against your neighbor. (9th Command)

17 "You shall not covet your neighbor's house. You shall not covet your neighbor's wife, or his male or female servant, his ox or donkey, or anything that belongs to your neighbor." (10th Commandment)

You may note that the Roman Catholic Church has a different numbering here. They break out the 10th into 2 as the 9th & 10th after combining the 1st and the 2nd into 1 as the 1st Commandment.