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### Chapter 5--Systems of Equations and Inequalities

 Essential Question:  How do we select and apply different and effective strategies for solving systems of linear equations and inequalities? Unit Rationale:  Building on previous experience with linear equations and inequalities will allow students to model and solve real-world problems involving comparison, rates, cost, etc. using systems of linear equations and inequalities. As a result of this unit, students will be able to: Ø  Solve a system of equations with different methods, and justify use of a specific method in a specific situation. Ø  Explain why a system of equations has zero, one or infinite solutions. Ø  Model a system of linear inequalities graphically.  Represent a verbal description as a system of equations. Ø  Solve a system of inequalities with different methods, and make choices about when to use a certain method. Ø  Solve an equation such as y=mx+b, y=ax+b, or d=rt for any variable. Vocabulary: ·        System of linear equations ·        System of inequalities ·        Substitution method ·        Elimination method ·        Feasible region ·        Sign-change rule Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements.  Focus Standards: *A1.1.B  Solve problems that can be represented by linear functions, equations, and inequalities. *A1.1.C  Solve problems that can be represented by a system of two linear equations or inequalities. Supporting Standards: *A1.4.A  Write and solve linear equations and inequalities in one variable *A1.4.D  Write and solve systems of two linear equations and inequalities in two variables. A1.2.E  Use algebraic properties to factor and combine like terms in polynomials. Reasoning, Problem Solving, and Communication Standards: A1.8.A  Analyze a problem situation and represent it mathematically. A1.8.B  Select and apply strategies to solve problems.