Solving Systems of Equations by Graphing

I love solving Systems of Equations! It is one of my favorite units to teach because the students get to use so many of things we have been learning all at once. 

We have already learned how to graph equations, but spent a day reviewing it before beginning this. We did a lot of talking about "solutions" and how they fit into equations. I struggle the most with students not understanding that the points on the line actually fit in the equation! We talk about that everyday during this unit, it eventually sticks with most of them. 

After a little exploration of just drawing graphs all over our coordinate plane, we finally realized that sometimes the lines will cross (one solution), sometimes they will never touch (no solution), and sometimes they will be the exact same line (infinite solutions).  From that we discussed slopes and y-intercepts and how they affect how our 2 lines will look. 

This is the final piece to our graphing systems discussion. Notes that we do together to show one of each type of solutions. We do this for graphing, substitution, and elimination.

Once the notes were done, they created pockets to sort the notes. This makes it easy to look back and see the commonality between one set of solutions.

The following day, after an assignment that turned out okay, I posted different systems of equations around the room. Each student had a graphing white board and worked through all 9 systems, they found their answer and then went to the sheet that had that answer. I was able to see their work and assist them if needed. It turned out to be a great activity that reinforced those who already got it and established a better foundation for those who were struggling.

 Some students worked faster than others, but because they had different starting spots, they couldn't tell what step their peers were on. It allowed everyone to work at their own pace. I also allowed the student who finished first to get out of the assignment that day.