algebra ii chapter 3: linear systems and vocabulary...
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Alg II Chapter 3 Notes.notebook
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August 22, 2014
Algebra IIChapter 3:
Linear Systems and Matrices
Vocabulary
Chapter 3 Lesson 1Solve Linear Systems by Graphing
Solutions
(0,5), (2.5,0), (1,3), etc
Alg II Chapter 3 Notes.notebook
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August 22, 2014
Example 1: Solve a System Graphically
ALWAYS USE STRAIGHT EDGES WHEN GRAPHING LINES!!!
You can check these with a calculator!1. Solve for y.2. Graph on Calculator.3. Press 2ND, then TRACE.4. Press 5, then ENTER, ENTER, ENTER.
Remind Gruver to give you the Algebra II graphing sheet!
Reminder: You are searching for the intersection point!!!!Your answer will be an ordered pair!
Example 2: Solve a System with Many Solutions
You can check these with a calculator!1. Solve for y.2. Graph on Calculator.3. Press 2ND, then TRACE.4. Press 5, then ENTER, ENTER, ENTER.
Seeing the equations in slopeintercept form can tell A LOT!*same slopes = parallel lines*same equation = same lines
Reminder: You are searching for the intersection point!!!!
Alg II Chapter 3 Notes.notebook
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August 22, 2014
Example 3: Solve a System with No Solution
You can check these with a calculator!1. Solve for y.2. Graph on Calculator.3. Press 2ND, then TRACE.4. Press 5, then ENTER, ENTER, ENTER.
Seeing the equations in slopeintercept form can tell A LOT!*same slopes = parallel lines*same equation = same lines
Reminder: You are searching for the intersection point!!!!
Example 4: Standardized Test Prep
You can check these with a calculator!1. Solve for y.2. Graph on Calculator.3. Press 2ND, then TRACE.4. Press 5, then ENTER, ENTER, ENTER.
Reminder: You are searching for the intersection point!!!!Your answer will be an ordered pair!
Alg II Chapter 3 Notes.notebook
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August 22, 2014
Chapter 3 Lesson 2Solve Linear Systems Algebraically
Vocabulary
Example 1: Use the Substitution Method
Reminder: You are searching for the intersection point!!!!Your answer will be an ordered pair!
Alg II Chapter 3 Notes.notebook
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August 22, 2014
Example 4: Solve Linear Systems with Many or No SolutionsReminder:If you end up with an identity (ex:1=1), there are infinite solutions.If you end up with something that is not equal, there are no solutions.
Example 2: Use the Elimination Method
Reminder: You are searching for the intersection point!!!!Your answer will be an ordered pair!
Alg II Chapter 3 Notes.notebook
6
August 22, 2014
Example 4: Solve Linear Systems with Many or No SolutionsReminder:If you end up with an identity (ex:1=1), there are infinite solutions.If you end up with something that is not equal, there are no solutions.
Example 3: Standardized Test PracticeIn order to save time, you should be thinking which method of solving might be fastest and/or easiest!
Alg II Chapter 3 Notes.notebook
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August 22, 2014
Chapter 3 Lesson 3Graph Systems of Linear InequalitiesVocabulary
Example 1: Graph a System in Two Inequalities
Use different colors!!!! It helps!!!
Reminders:
*solve for y first
*use dashed lines for < and >
*use solid lines < and >
*shade above when y>
*shade below when y<
Alg II Chapter 3 Notes.notebook
8
August 22, 2014
Example 2: Graph a System with No SolutionReminders:
*solve for y first
*use dashed lines for < and >
*use solid lines < and >
*shade above when y>
*shade below when y<
>
<
Use different colors!!!! It helps!!!
Example 3: Graph a System with an Absolute Value InequalityReminders:
*solve for y first
*use dashed lines for < and >
*use solid lines < and >
*shade above when y>
*shade below when y<
Use different colors!!!! It helps!!!
Absolute Value Graph Reminders!
*vertex at (h,k) (be careful of the sign of h!)
*a shrinks or stretches the graph
Alg II Chapter 3 Notes.notebook
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August 22, 2014
Example 4: Solve a MultiStep Problem
Chapter 3 Lesson 4Solve Systems of Linear Equations in Three VariablesVocabulary
Alg II Chapter 3 Notes.notebook
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August 22, 2014
Example 1: Use the Elimination Method
Reminder: You are searching for the intersection point!!!!Your answer will be an ordered triple!
Example 2: Solve a ThreeVariable System with No Solution
Reminder:If you end up with an identity (ex:1=1), there are infinite solutions.If you end up with something that is not equal, there are no solutions.
Alg II Chapter 3 Notes.notebook
11
August 22, 2014
Example 4: Solve a System Using SubstitutionThe Substitution Method for ThreeVariable System1. Solve one equation for a single variable.2. Rewrite the system as a linear system in two variables by substituting the value from step 1.3. Solve the system in step 2.4. Substitute the values from step 3 into one of the equations to find the final value.Reminder: You are searching for the intersection point!!!!Your answer will be an ordered triple!
Example 3: Solve a ThreeVariable System with Many Solutions
Reminder:If you end up with an identity (ex:1=1), there are infinite solutions.If you end up with something that is not equal, there are no solutions.
The Substitution Method for ThreeVariable System1. Solve one equation for a single variable.2. Rewrite the system as a linear system in two variables by substituting the value from step 1.3. Solve the system in step 2.4. Substitute the values from step 3 into one of the equations to find the final value.