1. **State the problem:** Gary ran 6 more laps than Edwin, and together they ran 40 laps. We need to check if the given statements and system of equations are true or false. 2. **Define variables:** Let $x$ be the number of laps Edwin ran. Let $y$ be the number of laps Gary ran. 3. **Write the system of equations from the problem:** - Gary ran 6 more laps than Edwin: $$y = x + 6$$ - Together they ran 40 laps: $$x + y = 40$$ 4. **Check the given system:** The given system is: $$y = x + 6$$ $$y = 40 - 6x$$ The second equation $y = 40 - 6x$ does not match the sum equation $x + y = 40$. 5. **Solve the correct system:** From $$y = x + 6$$ substitute into $$x + y = 40$$: $$x + (x + 6) = 40$$ $$2x + 6 = 40$$ $$2x = 40 - 6$$ $$2x = 34$$ $$x = \frac{34}{2} = 17$$ 6. **Find $y$:** $$y = x + 6 = 17 + 6 = 23$$ 7. **Interpret results:** Edwin ran 17 laps, Gary ran 23 laps. 8. **Check the statements:** - "A system of equations that represents this situation is $y = x + 6$ and $y = 40 - 6x$": **False** because the second equation is incorrect. - "Gary ran 17 laps and Edwin ran 11 laps": **False** because Gary ran 23 laps and Edwin ran 17 laps. - "Gary ran 23 laps and Edwin ran 17 laps": **True**. **Final answers:** - System of equations: False - Gary 17, Edwin 11: False - Gary 23, Edwin 17: True