Math Unit VII

MAT 1302, College Algebra 1

Course Learning Outcomes for Unit VII Upon completion of this unit, students should be able to:

3. Utilize algebraic principles to graph systems. 3.1 Investigate whether an ordered pair is a solution of a linear system in two variables. 3.2 Solve linear and nonlinear systems by the substitution and addition method. 3.3 Solve applications involving systems of linear equations in two variables.

6. Solve linear systems with two variables.

6.1 Graph linear and nonlinear inequalities in two variables. 6.2 Graph linear and nonlinear systems of inequalities.

Required Unit Resources Chapter 5: Systems of Equations and Inequalities, Sections 5.1, 5.4, 5.5

Unit Lesson This unit lesson provides an overview of concepts that you will learn in Unit VII as well as links to required lesson videos. For additional instruction and examples, please refer to Sections 5.1, 5.4, and 5.5 in your textbook. It is recommended to use the Unit VII Homework Videos Note-Taking Guide as you work through the videos.

Section 5.1: Systems of Linear Equations in Two Variables Assume that you are remodeling your home. You want to buy paint for each room and new carpet for each bedroom. You have a fixed budget of $3,000. If you know how much the carpet per square foot and paint per gallon costs, then you can create a system of equations to help you figure out how much paint and carpet you can afford. This scenario describes a system of linear equations in two variables where the variables represent the amount of paint and carpet. In this section, we will solve systems of linear equations in two variables. The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the videos. A transcript and closed captioning are available once you access the videos.

• Solutions to a System of Equations

• Solving Systems of Linear Equations Part I

• Solving Systems of Linear Equations Part II

• Applications of Systems of Linear Equations

Section 5.4: Systems of Nonlinear Equations in Two Variables We can expand our knowledge of systems of equations in two variables by looking at nonlinear systems. A nonlinear system is a system that contains at least one nonlinear equation. Examples of nonlinear equations are quadratic, cubic, and square-root equations.

UNIT VII STUDY GUIDE

Systems of Equations and Inequalities

MAT 1302, College Algebra 2

UNIT x STUDY GUIDE

Title

The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the videos. A transcript and closed captioning are available once you access the videos.

• Systems of Nonlinear Equations Part I

• Systems of Nonlinear Equations Part II

Section 5.5: Systems of Inequalities In Section 5.1, we learned that the point of intersection between two lines is a solution to the system of linear equations. In Section 5.4, we learned that there could be multiple solutions when two nonlinear equations or a nonlinear and linear equation intersect. In this section, we will examine linear and nonlinear inequalities and find the set of all solutions that fits the conditions given by the inequality sign. The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the videos. A transcript and closed captioning are available once you access the videos.

• Graphing Inequalities

• MyMathLab Graphing Tool for Inequalities

• Graphing Systems of Inequalities, Part I

• MyMathLab Graphing Tool for Systems of Inequalities

• Graphing Systems of Inequalities Part II

Additional Help Available If you find yourself needing additional assistance with course material, please know that the Math Center is available and ready to help. Click the Math Center Request form to get connected with the Math Center’s tutors.

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information.

Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study plan will update each time you take an assessment. The study plan is for extra practice. For assistance with course content, you may contact your instructor or a math specialist. Click the Student Resources link to find contact information for the Math Center.

MAT 1302, College Algebra 1

Course Learning Outcomes for Unit VII Upon completion of this unit, students should be able to:

3. Utilize algebraic principles to graph systems. 3.1 Investigate whether an ordered pair is a solution of a linear system in two variables. 3.2 Solve linear and nonlinear systems by the substitution and addition method. 3.3 Solve applications involving systems of linear equations in two variables.

6. Solve linear systems with two variables.

6.1 Graph linear and nonlinear inequalities in two variables. 6.2 Graph linear and nonlinear systems of inequalities.

Required Unit Resources Chapter 5: Systems of Equations and Inequalities, Sections 5.1, 5.4, 5.5

Unit Lesson This unit lesson provides an overview of concepts that you will learn in Unit VII as well as links to required lesson videos. For additional instruction and examples, please refer to Sections 5.1, 5.4, and 5.5 in your textbook. It is recommended to use the Unit VII Homework Videos Note-Taking Guide as you work through the videos.

Section 5.1: Systems of Linear Equations in Two Variables Assume that you are remodeling your home. You want to buy paint for each room and new carpet for each bedroom. You have a fixed budget of $3,000. If you know how much the carpet per square foot and paint per gallon costs, then you can create a system of equations to help you figure out how much paint and carpet you can afford. This scenario describes a system of linear equations in two variables where the variables represent the amount of paint and carpet. In this section, we will solve systems of linear equations in two variables. The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the videos. A transcript and closed captioning are available once you access the videos.

• Solutions to a System of Equations

• Solving Systems of Linear Equations Part I

• Solving Systems of Linear Equations Part II

• Applications of Systems of Linear Equations

Section 5.4: Systems of Nonlinear Equations in Two Variables We can expand our knowledge of systems of equations in two variables by looking at nonlinear systems. A nonlinear system is a system that contains at least one nonlinear equation. Examples of nonlinear equations are quadratic, cubic, and square-root equations.

UNIT VII STUDY GUIDE

Systems of Equations and Inequalities

MAT 1302, College Algebra 2

UNIT x STUDY GUIDE

Title

The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the videos. A transcript and closed captioning are available once you access the videos.

• Systems of Nonlinear Equations Part I

• Systems of Nonlinear Equations Part II

Section 5.5: Systems of Inequalities In Section 5.1, we learned that the point of intersection between two lines is a solution to the system of linear equations. In Section 5.4, we learned that there could be multiple solutions when two nonlinear equations or a nonlinear and linear equation intersect. In this section, we will examine linear and nonlinear inequalities and find the set of all solutions that fits the conditions given by the inequality sign. The following videos can be viewed here as well as in your homework assignment. Please click the titles below to view the videos. A transcript and closed captioning are available once you access the videos.

• Graphing Inequalities

• MyMathLab Graphing Tool for Inequalities

• Graphing Systems of Inequalities, Part I

• MyMathLab Graphing Tool for Systems of Inequalities

• Graphing Systems of Inequalities Part II

Additional Help Available If you find yourself needing additional assistance with course material, please know that the Math Center is available and ready to help. Click the Math Center Request form to get connected with the Math Center’s tutors.

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information.

Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study plan will update each time you take an assessment. The study plan is for extra practice. For assistance with course content, you may contact your instructor or a math specialist. Click the Student Resources link to find contact information for the Math Center.