SWBAT connect solving systems of equations by graphing to solving systems by substitution and discuss when using an equation is more accurate.

Connect solving systems of equations to real life baseball helmets and reading tables to find the equations for solving by substitution.

10 minutes

Write the following on the board:

*Martha and Winston (I like to use odd names just for fun) agree to meet at the park and go for a jog. Martha arrives on time and begins to run at a pace of six miles per hour. Winston is about five minutes late and seeing Martha already in the park he begins to jog at a pace of six miles per hour. How long will it take Winston to catch up to Martha?*

Allow students to discuss among themselves the answer, it shouldn't take very long, and then allow groups to share out their thinking. Challenge the class to sketch a graph of Distance over time for both Martha and Winston. Display a graph under the document camera and discuss what it means when the lines are parallel. Bring this discussion back to systems and that this is an example of a system of equations that has "no solution."

If you have time and want to extend this activity, you could challenge the class by asking them how fast Winston would have to run in order to catch up to Martha in 10 minutes. Hint, they could graph it to find the slope or use an equation.

30 minutes

10 minutes