CHAPTER Linear Equations and 4 Study Strategies: Taking Notes in Class 4.1 Solving Systems by Graphing 4.2 Solving Systems by the 4.3 Solving Systems by the Elimination Putting It All Together 4.4 Applications of Systems of Two Group Activity emPOWERme: Evaluate Your Class Notes 241 Inequalities in Two Variables OUTLINE Substitution Method Method Equations 4.5 Linear Inequalities in Two Variables Math at Work: Motorcycle Customization It takes both mechanical skill and artistic fl air to do what Frank Esposito does at work: customize motorcycles. It also takes knowledge of mathematical expressions and exponents. Indeed, the people who build and repair motor vehicles use a lot of mathematics on the job. For instance, suppose Frank takes apart a transmission to make repairs when he realizes that he has mixed up the gears. He is able to replace the shafts onto the bearings, but he cannot remember which gear goes on which shaft. Frank measures the distance (in inches) between the shafts, sketches the layout on a piece of paper, and comes up with a system of equations to determine which gear goes on which shaft. If x the radius of the gear on the left and y the radius of the gear on the right, then the system of equations Frank must solve to determine where to put each gear is x y 2.650 x y 0.746 Solving this system, Frank determines that x 1.698 in. and y 0.952 in. Now he knows on which shaft to place each gear. Frank doesn’t make mistakes like mixing up gears often. However, given how much technical information he has to remember and how many mechanical parts he has to deal with to do his job, some mistakes are inevitable. To minimize them, Frank makes a habit of writing down key pieces of information in a clear, organized way, allowing him to easily reference essential details later. You can use the same sorts of strategies to ensure the notes you take in class are effective. In this chapter, we will learn how to write and solve systems of two equations, and learn about taking good class notes.
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