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module 9

# module 9 - MAC 1140 Module 9 System of Equations and...

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Rev.S08 MAC 1140 Module 9 System of Equations and Inequalities I

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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 graphical and numerical methods to system of equations. 4. solve problems involving joint variation. 5. recognize different types of linear systems. 6. apply the elimination method. 7. solve systems of linear and nonlinear inequalities. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
3 Rev.S08 Learning Objectives (Cont.) 8. apply the method of substitution. 9. apply graphical and numerical methods to system of equations. 10. solve problems involving joint variation. 11. recognize different types of linear systems. 12. apply the elimination method. 13. solve systems of linear and nonlinear inequalities. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.

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4 Rev.S08 System of Equations and Inequalities I http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. 9.1 9.1 Functions and Equations in Two Variables Functions and Equations in Two Variables 9.2 9.2 System of Equations and Inequalities in Two System of Equations and Inequalities in Two Variables Variables 9.3 9.3 Systems of Linear Equations in Three Systems of Linear Equations in Three Variables Variables There are three sections in this module:
5 Rev.S08 Do We Really Use Functions of Two Variables? http://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.

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6 Rev.S08 Let’s Take a Look at the Arithmetic Operations http://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 .
7 Rev.S08 Here are Some Examples http://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 .

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