Saved by… obedience?

For years I've heard (and sometimes said) that salvation comes “by grace alone through faith alone in Christ alone.” So I was a little surprised to read in Hebrews 5 that Jesus “became the source of eternal salvation to all who obey him.” (emphasis added)

What's this about obedience? Does that contradict "by grace alone"? Maybe not.

Suppose you're in the middle of the ocean, after a plane crash or something, and can't see any land. A boat comes along, offering to save you. Sounds like grace to me! But when someone says, “Grab this rope,” you gotta obey and grab it.

If you instead say, “Wait, obedience? I thought this was by grace alone,” then you won't be saved. Silly, I know. But earlier in the letter, we read that faith and obedience come to the same thing.

[T]o whom did God swear that they would never enter his rest if not to those who disobeyed? So we see that they were not able to enter, because of their unbelief.

Hebrews 3:18–19 NIV (1984)

So no, we aren't saved by obedience; it really is by grace alone through faith alone. But if I'm unwilling to obey, that's not a disconnected random bit of information; it speaks to my lack of faith. And without faith … hey, without faith it's impossible to please God! Without faith, grace doesn't do me much good.

So it's not a paradox or a contradiction after all.

Update: the next morning

I opened my reading plan in the "Bible" app, where I read this:

... But the Hebrew word for 'faith' - emunah - is less about KNOWING, and more about DOING.

'Emunah' literally means "to take firm action", so to have faith is to act.

How about that! The Old Testament writers weren't confused at all about this the way we modern evangelicals sometimes are. Guess I shouldn't be surprised.