Module 7: Lesson 6

Module 7: Systems of Linear Equations

Lesson 6 Summary

In this lesson you investigated the following questions:

  • Why is it necessary to learn several methods for solving a problem?
  • How can you recognize which strategy is most appropriate for solving a given system of equations?

In the final lesson of this module you evaluated the strategies that you have learned for both modelling and solving linear systems. You revisited the problems that you previously modelled with linear systems in Lesson 2. You were able to confirm that the systems were properly set up. You also encountered a variety of other types of problems. You used what you learned previously about defining variables, organizing information, writing equations, and verifying solutions to solve the problems in this lesson.

In this lesson you worked with your peers to compare the strategies, determining both the benefits of drawbacks of each one. By having multiple strategies in your repertoire, you become more prepared to tackle a variety of problems. You may have discovered that some strategies work better with certain problem types, while other strategies are suited to other types of problems. By learning several solution strategies, you can choose one that enables you to solve the problem.

The benefit of the graphing method is that it can help you to visualize the solution. The graphing method is best suited to those systems whose equations are easily graphed. The drawback of this method is that it does not always provide an exact solution. You can improve the precision of the solution values by using graphing technology. However, unless the point of intersection occurs at a lattice point, you will be forced to estimate the solution. Sometimes it is difficult to know if graphing is going to provide a suitable solution until you have already graphed the system.

The algebraic methods that you learned in this module, including substitution and elimination, can provide exact solutions. The method of substitution is suited for questions where a variable is already isolated or can easily be isolated. On the other hand, the method of elimination can be employed in all other situations, particularly those situations where the coefficients of the like terms in each equation match.

Ultimately, the strategy that you choose to solve a problem is based on personal preference. It is important, however, to learn several ways of approaching a problem as you continue your math studies. This will prepare you for a greater array of problem-solving demands and give you the confidence to tackle them efficiently.

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