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### Ideas from Classroom Teachers forSystems of Linear Equations and Inequalities

A review of graphing linear equations is a good starting point. Discussing what the solution to an equation looks like is needed before students can understand the solution of a system of equations. Later, discussion of solutions to a system of inequalities is necessary: "What does the solution mean? What have we found?"

Solving linear equations algebraically should go hand in hand with solving them graphically. Students may think that only the algebraic solution is the "real mathematical" solution. The A’‘ students, especially, need to solve systems graphically and algebraically at the same time so they can see the relationship – one is a picture of the other.

Models developed in A.1.4 can be used to show two patterns compared to one another; e.g., which company should I rent a trailer from?

Using many rich problems or real-world applications will help to make sense of the data. Pizza Pi: Work Force, a lesson available at http://www.hsor.org/modules.cfm?name=Pizza_Pi is a good linear programming problem that can be used with this topic.

Use of graphing calculators or some other graphing software program is a plus in teaching this section. When students set up the window menu, they are forced to think about what span of numbers their graph is covering.

Good practice: Solve one system all three ways. Do this for several problems. This will help the student decide which method is best for which situation. Discuss advantages and disadvantages of each method (graphical and algebraic methods).

Have students look at a system before trying to solve it for cues as to whether the system might be dependent or inconsistent.

Linear programming problems should be very basic, so the usefulness is not overshadowed by the difficulty.

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