Upvote:6
These two slogans were used to explain two major disagreements Protestants had with what the Catholic Church was teaching, and yes, they are designed to work together! They don't compete, they are alone in their own respective fields.
Sola Fide refers to the belief that works are not a means or prerequisite for salvation. People are declared to be justified (righteous) purely on the basis of trusting God to fulfil his promise to save us through the gracious act of Jesus taking the hit for us on the cross. This was the major defining belief of the Protestant reformation.
Sola Gratia refers to the belief that nothing a person does contributes to their salvation. From God's perspective no person has ever merited any component of their salvation - salvation is purely a gift (grace) from God. There is a lot of overlap between this and Sola Fide. But it means that the game never changes. Once you're saved you still live on the basis of grace and faith. The good works Christians do will never be anything other than graces from God. I've also heard that it is a kind of summary of the other Solas: Our faith is a gift from God, not something we produce ourselves. Christ Alone means we come to God purely through Jesus, with no human mediators. Grace Alone means that Jesus was never obligated to do anything, especially not come to the earth and die - every action of God is a gift. Similarly God was never obligated to reveal himself to us through scripture - the Bible is a gift.
The two work together, and many Protestants will say that we are saved "by grace through faith", exactly what your verse from Ephesians says.