This week’s Friday Fave requires a little help from your friends.
System of Two Linear Equations
begins by asking a simple question:
*Is it possible for two numbers to have a difference of 8, but a sum of
1?*

We’re not asking for examples at this point, nor are we expecting you to
have techniques ready at hand. We’re just asking for your instincts, and in a
sufficiently large class of algebra students we expect some *yeses*,
several *nos*, and quite a few *maybes*. Discuss.

Next up, we’ll get specific. Think of two numbers with a difference of 8 and give us the larger one. We’ll guess the second one, plot them both as an ordered pair and ask you to think about what the collection of everyone’s points will look like.

You see what we did there? We created a social experience by connecting you with your friends to discuss some informal ideas, and then we made those informal ideas more formal one step at a time. Pretty soon, you’re writing equations for lines and noticing that their intersection is a number pair whose difference is 8 and whose sum is 1.

More constraints and opportunities to think, share, collaborate, and discuss
follow. An informal question—*Is it possible?*—introduces an invitation
to develop some important algebraic techniques.

That’s what makes System of Two Linear Equations this week’s Friday Fave, and while you’re thinking of systems of equations (and inequalities!) here are a few more activities to play with.