Lesson 5

Lesson 5 Summary

 

In this lesson you investigated the following questions:

• Why are the points of intersection of a system of equations related to its solution?
  
  
• How does a graphical representation facilitate mathematical understanding?

You studied graphical methods of solving systems of linear-quadratic and quadratic-quadratic equations. As in the case of linear systems that you studied previously, the solutions to quadratic systems are found at the points of intersection. This is due to the fact that such points lie on both graphs and therefore satisfy both equations simultaneously.

 

Throughout this lesson, you used graphs to represent the systems. You learned how to model problems using both linear-quadratic and quadratic-quadratic systems. In many cases, you used a sketch or drawing to help you visualize the problem. By doing so, you were able to better connect the nature of the problem to the math underlying the solution.

 

In the next lesson you will continue to work with quadratic systems. You will explore methods of solving these systems algebraically.