I am trying to review key algebra 1 concepts as well as move forward with the new stuff. We do not teach linear combination in algebra 1, because it takes all of our effort to just get across the idea of solving a system graphically and algebraically (through substitution), and how the graph is related to the algebra.

In my next lesson, I will start by reviewing the substitution method a bit more, with an example that causes lots of fractions to form. Then I will introduce the idea of linear combination through 3 progressively harder examples (i.e. needing to multiply neither, then one, then both equations for it to work out).

Finally, students will work in pairs on basic practice problems. The only innovation I have here over last year is that I am requiring students to explicitly answer these questions before beginning to solve each system:

1) Is there anything you can do to simplify either equation (i.e. can you divide out the GCF, or multiply by the LCD to clear the denominators?)

2) Which variable will you eliminate?

3) Which equation (if any) will you multiply, and by what factor?

So no need to post anything on ILoveMath . But I'm hoping that forcing students to answers those questions will help them clarify the process in their minds.

A beautiful combinatorics argument

11 hours ago

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