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Unformatted text preview: 1 Rev.S08 MAC 1105 Module 3 System of Equations and Inequalities 2 Rev.S08 Learning Objectives Upon completing this module, you should be able to: 1. Evaluate functions of two variables. 2. Apply the method of substitution. 3. Apply the elimination method. 4. Solve system of equations symbolically. 5. Apply graphical and numerical methods to system of equations. 6. Recognize different types of linear systems. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. 3 Rev.S08 Learning Objectives (Cont.) 7. Use basic terminology related to inequalities. 8. Use interval notation. 9. Solve linear inequalities symbolically. 10. Solve linear inequalities graphically and numerically. 11. Solve double inequalities. 12. Graph a system of linear inequalities. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. 2 4 Rev.S08 System of Equations and Inequalities ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. System of Linear Equations in Two Variables System of Linear Equations in Two Variables Solutions of Linear Inequalities Solutions of Linear Inequalities There are two major topics in this module: 5 Rev.S08 Do We Really Use Functions of Two Variables? ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. The answer is YES. Many quantities in everyday life depend on more than one variable. Examples Area of a rectangle requires both width and length. Heat index is the function of temperature and humidity. Wind chill is determined by calculating the temperature and wind speed. Grade point average is computed using grades and credit hours. 6 Rev.S08 Let’s Take a Look at the Arithmetic Operations ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. The arithmetic operations of addition, subtraction, multiplication, and division are computed by functions of two inputs . The addition function of f can be represented symbolically by f ( x,y ) = x + y , where z = f ( x,y ) . The independent variables are x and y . The dependent variable is z . The z output depends on the inputs x and y . 3 7 Rev.S08 Here are Some Examples ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. For each function, evaluate the expression and interpret the result. a) f (5, –2) where f ( x,y ) = xy b) A (6,9), where calculates the area of a triangle with a base of 6 inches and a height of 9 inches. Solution • f ( 5 , –2 ) = ( 5 )( –2 ) = –10. • A (6,9) = If a triangle has a base of 6 inches and a height of 9 inches, the area of the triangle is 27 square inches . 8 Rev.S08 What is a System of Linear Equations?...
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This note was uploaded on 10/18/2011 for the course MAC 1105 taught by Professor Russel during the Summer '07 term at Valencia.
 Summer '07
 RUSSEL
 Algebra, Equations, Inequalities

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