# PreCalc Chapter 8

Ch 8 Systems of Equations and Inequalities

Ch 8.1 Systems of Equations

Steps of Solving a System of Linear Equations using Substitution Method ;
Solving  and using Substitution Method ;
Solving  and  using Substitution Method ;
Solving  and  using Graphing Calculator ;
Solving  and  using Substitution Method ;
Solving  and  using Substitution Method

Solving the Following Systems of Equations Using the Substitution Method and Graphing Method  and  ;
and
http://www.youtube.com/watch?v=_teT7HKc0mQ&list=PL554F9F460401DF50&index=34&feature=plpp_video (Part 1 and 2 of the Video)

Ch 8.2 Systems of Linear Equations in Two Variables

Solving  and  using Method of Elimination ;
Steps of Solving a Systems of Linear Equations using Method of Elimination ;
Solving  and  using Method of Elimination ;
Solving  and  using Method of Elimination ;
Finding the Numbers of Minutes for Two Phone Plans which Cost the same

Solving  and  using Method of Elimination ;
Solving  and  using Method of Elimination ;
Solving  and  using Method of Elimination ;
Three Possible Solutions : Exactly One Solution, An Infinite Number of Solutions, No solution
http://www.youtube.com/watch?v=_teT7HKc0mQ&list=PL554F9F460401DF50&index=34&feature=plpp_video (Part 3, 4, and 5 Video)

Solving  and  using Method of Elimination

Solving  and   using Method of Elimination with Infinite Solutions

Solving  and  using Method of Elimination with No Solutions

Finding the Intersection of Two Curves using the TI-83/84 Calculator

Ch 8.3 Systems of Inequalities

Finding Solutions and Graphing  ;
Solving Linear Inequality ;
Graphing the System  ,  ,  ,  ;
Graphing the System  ,

Steps of Graphing a Linear Inequality ;
Graphing Inequality  ;
Writing an Inequality to Describe the Graphs ;
Word Problem : Writing an Inequality to Represent the Total Cost of the Seeds, Graphing the Inequality, and Using the Graph to Answer the Questions

Graphing Inequality  ;
Writing an Inequality to Describe the Graph of Inequality ;
Word Problem : Graphing the Inequality that Represents the Relationship of Two Numbers

Graphing and Solving the Inequalities of  and  ;
Graphing and Solving the Inequalities of  and  ;
Graphing and Solving the Inequalities of  and

Graphing and Solving the Inequalities of  and

Graphing and Solving the Inequalities of  and

Graphing and Solving the Inequalities of  and  ,  , and

Ch 8.4 Linear Programming

Minimizing  Subjecting to the Constraints ,  and

Linear Programming on Maximizing Profits for Planting Corns and Oats

Linear Programming on Minimizing Cost for Breeding Two Different Brands of Food for Cattle

Ch 8.5 Systems of Linear Equations in More than Two Variables

Solving the System of Equations using Elimination

Introduction to Augmented Matrices (Row Echelon Form) ;
Writing ,  and  as an Augmented Matrix ;
Solving  and  using Row Echelon Form ;

Augmented Matrices: Row Echelon Form
Solving  and  ;
Solving  ,  and

Solving a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
and
and
and

Solving a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
,  and
,  and

Introduction to Augmented Matrices (Reduced Row Echelon Form) ;
Solving  and  using Reduced Row Echelon Form ;
Solving ,  and  using Reduced Row Echelon Form

Solving a System of Two Equations with Using an Augmented Matrix (Reduced Row Echelon Form)
and
and
and

Solving a System of Three Equations with Using an Augmented Matrix (Reduced Row Echelon Form)
and  and

Augmented Matrices on the Calculator TI83/84

Ch 8.6 The Algebra of Matrices

Definition of Matrix ;
Matrix Addition, Subtraction, and Scalar Multiplication
Identifying the Elements , , ,  in the Matrix     ;
Determining , ,  of Matrices  ,  ,  ;
Determining  of Matrix  ;
Determining ,  of Matrices  ,  ,  ,

Subtracting

Multiplying  ;
Finding  if

Multiplying  given Matrix  and

Application of Matrix Multiplication: Transformations of  and

Ch 8.7 The Inverse of a Matrix

Showing Matrix  is the Inverse of Matrix  and Matrix  is the Inverse of ;
Finding the Inverse Matrix of  ;
Finding the Inverse Matrix of

Finding the Inverse Matrix of

Finding the Inverse Matrix of

Finding the Inverse Matrix of

Ch 8.8 Determinants

Definition of Determinant of a Matrix ;
Finding the Determinants of  ;
Finding the Determinants of  ;
Finding Determinants of  using Diagonal Method ;
Finding Determinants of  using Method of Cofactors

Finding Determinants of  using Method of Cofactors

Finding the Determinants of  using Method of Cofactors

Ch 8.9 Properties of Determinants

Using Cramer’s Rule to Solve the Systems of Equations ;
Solving the System of  and  using Cramer’s Rule ;
Solving the System of ,  and  using Cramer’s Rule

Solving the System of  and  using Cramer’s Rule

Solving the System of ,  and  using Cramer’s Rule

Application of Determinants: Area of Triangle and Parallelogram on the Coordinate Plane

Ch 8.10 Partial Fractions

Steps of Performing Partial Fraction Decomposition ;
Setting Up Partial Fraction Decomposition of Rational Expressions  ,  and

Finding Partial Fraction Decomposition of Rational Expression

Finding Partial Fraction Decomposition of Rational Expression   Containing a Linear Factor

Finding Partial Fraction Decomposition of Rational Expression  Containing a Linear Factor