235 Systems of Linear Equations and Inequalities 3 CHAPTER OUTLINE 3.1 Solving Systems of Linear Equations by the Graphing Method 236 3.2 Solving Systems of Linear Equations by the Substitution Method 246 3.3 Solving Systems of Linear Equations by the Addition Method 253 Problem Recognition Exercises: Solving Systems of Linear Equations 260 3.4 Applications of Systems of Linear Equations in Two Variables 261 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables 270 3.6 Systems of Linear Equations in Three Variables and Applications 283 3.7 Solving Systems of Linear Equations by Using Matrices 293 Group Activity: Creating a Quadratic Model of the Form y at2 bt c 302 Chapter 3 In this chapter, we solve systems of linear equations in two and three variables. One of the skills we need is to find the point of intersection between two lines. Are You Prepared? To practice, graph the five lines on the grid provided. Then answer the questions and place the letter corresponding to each answer in the space below. This will define an important vocabulary word for this chapter. Line 1. y x 2 Line 2. y x 4 Line 3. x y 1 Line 4. y 2 Line 5. x 4 1 2 1. The point of intersection between lines 1 and 2. 2. The point of intersection between lines 3 and 4. 3. The point of intersection between lines 5 and 1. 4. The line that is parallel to line 3. 5. The line that is vertical. 6. The line that has (3, 1) as a solution. 7. The point of intersection between lines 1 and 3. A ___ ___ ___ ___ ___ ___ ___ ___ to a system of linear equations is a point of 4 1 5 6 2 3 1 7 intersection between two lines. y x 5 4 3 2 1 5 4 2 1 1 2 3 4 5 1 3 4 5 3 T (1, 2) I (3, 1) U Line 2 O (1, 3) S Line 1 N no point of intersection L Line 5
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