How Many Solutions?

I’ve been thinking about systems of linear equations for the past couple of days. Most of my focus has been on systems of two equations, but this morning I wrote a question about a system of three linear equations that might spark some interesting and revealing classroom conversations:

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And now I’m wondering…

  • How many solutions does that system have? Drop your thoughts in the comments, would you?
  • If you put this prompt in front of your students, I’d love to hear a recap of how that plays out.