Do Jesus’ Words Take Precedence over Everything Else in Scripture?

Questions about how to respond to friends who say that Jesus’ words take precedence over everything else in Scripture and anything he didn’t speak on isn’t worth discussion, what to do with the Old Testament, and how to tell which of its promises are for us.  

• How should I respond to friends who say that Scripture is all true but Jesus’ words take precedence over the rest, and that anything he didn’t speak on isn’t worth discussion?
• If the Old Testament isn’t written to us, what do we do with it? Why use it? Are any of the promises of the Old Testament for us, and if so, how can you tell the difference?