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4.1 Solving Systems of Linear Equations Graphically and Numerically 4.2 Solving Systems of Linear Equations by Substitution 4.3 Solving Systems of Linear Equations by Elimination 4.4 Systems of Linear Inequalities
Systems of Linear Equations in Two Variables
We can do anything we want to do if we stick to it long enough.
—HELEN KELLER
mericans have been moving toward a more mobile lifestyle. In recent years, the percentage of U.S. households relying solely on mobile phone service has increased, while the percentage of households relying solely on landline phone service has decreased. The following figure shows that linear equations can be used to model the percentage P of households relying on each type of phone service during year x. What does the point of intersection represent?
Telephone Service
P
40
A
Percent of Households
Landline-only Households
30 20 10 0 ’05 ’06 ’07 ’08 ’09 ’10
Wireless-only Households
x
Year
ISBN 1-256-49082-2
Source: National Center for Health Statistics.
This graph illustrates a system of linear equations. If we use the graph to estimate both the year and the percentage at the intersection point, we are solving the system of linear equations graphically. In this chapter we discuss graphical, numerical, and symbolic methods for solving systems of linear equations.
245
Beginning and Intermediate Algebra with Applications & Visualization, Third edition, by Gary K. Rockswold and Terry A. Krieger. Published by Addison Wesley. Copyright © 2013 by Pearson Education, Inc.
246
CHAPTER 4 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
4.1
Solving Systems of Linear Equations Graphically and Numerically
Basic Concepts ● Solutions to Systems of Equations
A LOOK INTO MATH N
In business, linear equations are sometimes used to model supply and demand for a product. For example, if the price of a gourmet coffee drink is too high, the demand for the drink will decrease because consumers are
4.1 Solving Systems of Linear Equations Graphically and Numerically 4.2 Solving Systems of Linear Equations by Substitution 4.3 Solving Systems of Linear Equations by Elimination 4.4 Systems of Linear Inequalities
Systems of Linear Equations in Two Variables
We can do anything we want to do if we stick to it long enough.
—HELEN KELLER
mericans have been moving toward a more mobile lifestyle. In recent years, the percentage of U.S. households relying solely on mobile phone service has increased, while the percentage of households relying solely on landline phone service has decreased. The following figure shows that linear equations can be used to model the percentage P of households relying on each type of phone service during year x. What does the point of intersection represent?
Telephone Service
P
40
A
Percent of Households
Landline-only Households
30 20 10 0 ’05 ’06 ’07 ’08 ’09 ’10
Wireless-only Households
x
Year
ISBN 1-256-49082-2
Source: National Center for Health Statistics.
This graph illustrates a system of linear equations. If we use the graph to estimate both the year and the percentage at the intersection point, we are solving the system of linear equations graphically. In this chapter we discuss graphical, numerical, and symbolic methods for solving systems of linear equations.
245
Beginning and Intermediate Algebra with Applications & Visualization, Third edition, by Gary K. Rockswold and Terry A. Krieger. Published by Addison Wesley. Copyright © 2013 by Pearson Education, Inc.
246
CHAPTER 4 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
4.1
Solving Systems of Linear Equations Graphically and Numerically
Basic Concepts ● Solutions to Systems of Equations
A LOOK INTO MATH N
In business, linear equations are sometimes used to model supply and demand for a product. For example, if the price of a gourmet coffee drink is too high, the demand for the drink will decrease because consumers are