Why did African slavery immediately become the dominant labor system in South Carolina, while it was slow to dominate in the other Southern colonies

Keep in mind this is a pretty specific question, and your
instructor may be looking for a specific response from class notes or your textbook.  In my
opinion, there were two key reasons slavery so quickly became the dominant aspect of the South
Carolinian economy:

1) Charleston, South Carolina was the largest
entry port in the colonies for slaves from Africa and the West Indies, therefore slaves were
somewhat cheaper and more readily available in that particular
colony.

2) South Carolina farmed different cash crops than North
Carolina and Virginia, specifically indigo and rice.  Slaves were imported to South Carolina from
tribes that already farmed rice in Africa, giving them a skilled labor force that needed little
training.  This simply accelerated the economy's dependence on slave labor in that
location.

In other colonies north of there, plantation owners had
experimented with indentured servants as a labor force for a time as the tobacco economy
developed there.  By the 1670s when the Carolinas were settled, large scale indentured servitude
had been abandoned in favor of the more economical slavery.

South
Carolina also engaged in the export of Indians as slaves for quite some time, and tens of
thousands were exported for other labor markets in the late 1600s and early 1700s, so in addition
to slaves on plantations, the slave trade itself was central to its early
economy.