Final answer:
The Roman Catholic Church responded to Luther and Calvin by maintaining that salvation was through both faith and works, differing from Luther's faith alone and Calvin's predestination doctrines. They codified their stance at the Council of Trent.
Step-by-step explanation:
The Roman Catholic Church replied to the doctrines of Luther and Calvin by reasserting its stance that salvation was through both faith and works. While Martin Luther determined that salvation was by faith alone, the Catholic Church maintained that both faith and good works were essential for one's salvation. This was a counterargument to Luther's doctrine of justification by faith as well as John Calvin's doctrine of predestination. Moreover, in response to these Protestant Reformation leaders, the Council of Trent (1545-1563), as part of the Counter-Reformation, codified the Catholic Church's position on salvation, rejecting the sole sufficiency of faith for salvation as proposed by Luther and similarly refuting Calvin's views on the absence of free will in matters of faith.
Calvin emphasized his belief in predestination, suggesting that the fate of each soul was predetermined by God. However, the Catholic Church disagreed and upheld that human beings have the potential to influence their own salvation through both faith and the good works, standing in contrast to the doctrines of Luther and Calvin.