Chapter 3 Note Packet on Linear Systems

Chapter 3 Note Packet on Linear Systems

Day 1: 3-1 Solving Linear Systems by graphing and 3-3 Graphing Linear Inequalities

Practice: In 1-2, Consider the system: . Determine if each ordered pair is a solution to the system:

1. (1, 2) 2. (7, 6)

Solving a system of linear equations by graphing.

Practice: In 1-2, Graph the linear system and state the solution. Then check the solution algebraically.

1. 2.

Types of Linear Systems

· Linear systems that have a solution or many solutions are said to be consistent.

o Linear systems that have only one solution are also called independent.

o Linear systems that have many solutions are also called dependent.

· Linear systems that have no solution are said to be inconsistent.

Practice: In 1-3, Solve the system by graphing. Then classify the system as consistent and independent, or consistent and dependent, or inconsistent.

1. 2. 3.

Graph to #1 Graph to #2 Graph to #3

To Graph Systems of Linear (and absolute value) Inequalities.

Practice: In 1- 3, Graph the system of inequalities and state an ordered pair that is a solution, if possible.

1. 2. 3.

Day 2 Section 3-2 Solving Linear Systems Algebraically

There are two types of algebraic methods to solve systems of linear equations: 1) The substitution method and 2) The elimination method.

Method 1: The Substitution Method

Practice: In 1-2, solve the system using the substitution method

1. 2.

Method 2: The Elimination (addition) Method

Practice: In 1-2, solve the system using the elimination method

1. 2.

Solving systems algebraically that have many or no solutions.

Practice: In 1-2, solve the system using either the substitution or elimination method

1. 2.

Day 3: Section 3-4 Solve Systems of Linear Equations in Three Variables

Practice: In 1-2, determine whether the given ordered triple is a solution of the system.

1. (1, 4, 2): 2. (7, −1, 0):

Elimination Method for 3-Variable Systems

Practice: In 1-2, Solve the system using the elimination method

1. 2.

Substitution Method for 3-Variable Systems

Practice: In 1-2 Solve the system using the substitution method

1. 2.

Review for Chapter 3

Please complete each problem on a separate sheet of paper. Show all of your work! NO WORK = NO CREDIT!

For questions 1-2, find the vertex of the graph of the following functions, determine whether the graph of the function opens up or down, state whether the graph is wider, narrower, or the same width as the graph of y = |x|. Then graph the function.

1. 2.

For questions 3-4, solve the system by graphing.

3. 4.

For questions 5-6, solve the system by substitution.

5. 6.

For questions 7-8, solve the system by elimination (linear combination) method.

7. 8.

For questions 9-10, graph each system of inequalities.

9. 10.

For questions 11-12, solve each system of equations by elimination or substitution.

11. 12.

For questions 13-15, simplify each expression.

13. 14.

15.

For questions 16-17, solve each equation.

16. 17.

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