My New Way of Solving Systems of Equations

I Googled “system of equations” and took the first one I saw and worked on it.

I was doing something else with number lines when I suddenly realized that using the number line to solve systems is something no one has mentioned before. (A quick Google search didn’t yield anything. To solve for one equation, yes, but not a system.)

We show students various strategies: elimination, graphing, substitution, and eyeballing. I’m not sure why we don’t start with something that students are already familiar with—a number line. We use it to help students count forward and backward, add and subtract, scale, and all the great things related to #clotheslinemath from Kristen and Chris.

The strategy is not necessarily faster or slower than another but is grounded in the important visual. Equally important is the concept of distance on the number line is preserved. If I had abbreviated or eliminated some stuff, I could have done it faster than the work shown above, but I wanted to show you the full process.

Here’s another random one from the Internet and my work.

1. I get the coefficient of x or y to be the same, and both equations are in standard form.

2. Place this common term [6y] on the number line.

3. I see 6y + 6x gets me to 0, so I mark that.

4. I see 6y - 21x put me at 54; I mark that. (Not to scale.)

5. The distance between the quantities is 27 x units equals 54, so each x is 2.

6. I changed 2 to negative 2 because we’re dealing with the number line, and 54 should not be to the left of 0, but it is here, so I need to adjust.