Lesson Menu Five-Minute Check (over Chapter 5) TEKS Then/Now New Vocabulary Concept Summary: Possible Solutions Example 1:Number of Solutions Example 2:Solve.

Slides:

Advertisements

Similar presentations

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–1) CCSS Then/Now New Vocabulary Key Concept: Solving Systems of Inequalities Example 1: Intersecting.

Advertisements

Math Pacing Graphing Systems of Equations. Many real-world problems can be solved using a system of equations.

Graphing Systems Of Equations Lesson 6-1 Splash Screen.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 6–1) CCSS Then/Now New Vocabulary Key Concept: Solving by Substitution Example 1:Solve a System.

Solve Systems of Equations By Graphing

Solving Systems of Linear Equations by Graphing

Solving Systems of Linear Equations Graphically

Slide Systems of Linear Equations A system of linear equations consists two or more linear equations.

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 5) CCSS Then/Now New Vocabulary Concept Summary: Possible Solutions Example 1:Number of Solutions.

6.1 Graphing Systems of Equations

Over Lesson 8–9 A.A B.B C.C D.D 5-Minute Check 1 Which is an equation for the line of best fit for the scatter plot where x is the years since 1998 and.

Solve Systems of Linear Equations Graphically Honors Math – Grade 8.

Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

SOLVING SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.

Lesson 7-1 Graphing Systems of Equations. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

System of Linear Equations with One Solution Solve the given system of linear equations by graphing both equations on the same integer screen. 1. The point.

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 2) Then/Now New Vocabulary Example 1:Solve by Using a Table Example 2:Solve by Graphing Example.

Objective : Solving systems of linear equations by graphing System of linear equation two or more linear equations How do I solve linear systems of equations?

7-1 Graphing Systems of Equations SWBAT: 1) Solve systems of linear equations by graphing 2) Determine whether a system of linear equations is consistent.

3.1 WARM-UP Graph each of the following problems

Monday, March 23 Solve system of linear equations by graphing. Check consistency and dependency of system of equations by graphing.

Chapter 13 Section 2 Solutions of Systems of Equations.

6-1: Graphing Systems of Equations. Solve the inequality: -7x < -9x x < 2 2. x > 2 3. x < 7 4. x > 9.

3.1 Solving Systems Using Tables and Graphs When you have two or more related unknowns, you may be able to represent their relationship with a system of.

LESSON 6–6 Systems of Inequalities. Lesson Menu Five-Minute Check (over Lesson 6–5) TEKS Then/Now New Vocabulary Example 1:Solve by Graphing Example 2:No.

Lesson Menu Five-Minute Check (over Chapter 2) CCSS Then/Now New Vocabulary Example 1:Solve by Using a Table Example 2:Solve by Graphing Example 3:Classify.

3.1 Graphing Systems of Equations Objective – To be able to solve and graph systems of linear equations. State Standard – 2.0 Students solve systems of.

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 5) CCSS Then/Now New Vocabulary Concept Summary: Possible Solutions Example 1:Number of Solutions.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–9) Then/Now New Vocabulary Example 1: Solve by Graphing Example 2: Standardized Test Example.

Graph of a System Number of Solutions Exactly one solution Infinitely manyNo Solutions TerminologyConsistent and Independent Consistent and Dependent Inconsistent.

6-1 Solving Systems by Graphing AGAIN Goals: Interpret solutions for special problems. Model a real-life problem using a linear system. Eligible Content:

LESSON 6–1 Graphing Systems of Equations. Lesson Menu Five-Minute Check (over Chapter 5) TEKS Then/Now New Vocabulary Concept Summary: Possible Solutions.

Chapter 3 – Linear Systems 3-1 Solving Systems Using Tables and Graphs.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

Solving Systems of Equations By Graphing (6-1) Objective: Determine the number of solutions a system of linear equations has, if any. Solve a linear system.

Objective: To solve a system of linear equations by graphing and substitution.

Content Standards A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions.

3.5 Solving systems of equations in three variables Main Ideas Solve systems of linear equations in three variables. Solve real-world problems using systems.

Lesson 4-1 Solving linear system of equations by graphing

3-1 Graphing Systems of Equations

How do you solve a system of equations with graphing?

Scatter Plots and Lines of Fit

Classifying Systems, Solving Systems by Graphing and Substitution

Optimization with Linear Programming

LESSON 6–2 Substitution.

Consistent and Dependent Systems

Solving Systems of Linear Equations and Inequalities

Special Cases Involving Systems

Five-Minute Check (over Lesson 3–1) Mathematical Practices Then/Now

Notes for Algebra 1 Chapter 6.

Warm - Up Graph each equations on its own coordinate plane.

Graphing Systems of Equations

7.1 System of Equations Solve by graphing.

Systems of Equations Solving by Graphing.

Indicator 16 System of Equations.

Chapter 6 Vocabulary (6-1)

1.2 Solving Linear Systems by Graphing

Objective: Students will solve systems by graphing

Chapter 9 Lesson 3 Pg. 699 Solving Systems of Equations by Graphing

Chapter 9 Lesson 3 Pg. 699 Solving Systems of Equations by Graphing

4 Chapter Chapter 2 Solving Systems of Linear Equations.

Presentation transcript:

Lesson Menu Five-Minute Check (over Chapter 5) TEKS Then/Now New Vocabulary Concept Summary: Possible Solutions Example 1:Number of Solutions Example 2:Solve by Graphing Example 3:Real-World Example: Write and Solve a System of Equations

Over Chapter 5 5-Minute Check 5 A.12 nickels B.11 nickels C.10 nickels D.9 nickels Lori had a quarter and some nickels in her pocket, but she had less than $0.80. What is the greatest number of nickels she could have had?

TEKS Targeted TEKS A.3(F) Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist. A.3(G) Estimate graphically the solutions to systems of two linear equations with two variables in real- world problems. Also addresses A.2(I) and A.5(C). Mathematical Processes A.1(D), A.1(G)

Then/Now You graphed linear equations. Determine the number of solutions a system of linear equations has. Solve systems of linear equations by graphing.

Vocabulary system of equations consistent independent dependent inconsistent

Concept

Example 1A Number of Solutions A. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. y = –x + 1 y = –x + 4 Answer: The graphs are parallel, so there is no solution. The system is inconsistent.

Example 1B Number of Solutions B. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. y = x – 3 y = –x + 1 Answer: The graphs intersect at one point, so there is exactly one solution. The system is consistent and independent.

Example 1A A.consistent and independent B.inconsistent C.consistent and dependent D.cannot be determined A. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. 2y + 3x = 6 y = x – 1

Example 1B A.consistent and independent B.inconsistent C.consistent and dependent D.cannot be determined B. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. y = x + 4 y = x – 1

Example 2A Solve by Graphing A. Graph each system and determine the number of solutions that it has. If the system has one solution, name it. y = 2x + 3 8x – 4y = –12 Answer: The graphs coincide. There are infinitely many solutions of this system of equations.

Example 2B Solve by Graphing B. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. x – 2y = 4 x – 2y = –2 Answer: The graphs are parallel lines. Since they do not intersect, there are no solutions of this system of equations.

Example 2A A.one; (0, 3) B.no solution C.infinitely many D.one; (3, 3) A. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

Example 2B A.one; (0, 0) B.no solution C.infinitely many D.one; (1, 3) B. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

Example 3 Write and Solve a System of Equations BICYCLING Naresh rode 20 miles last week and plans to ride 35 miles per week. Diego rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Naresh and Diego will have ridden the same number of miles.

Example 3 Write and Solve a System of Equations

Example 3 Write and Solve a System of Equations Graph the equations y = 35x + 20 and y = 25x The graphs appear to intersect at the point with the coordinates (3, 125). Check this estimate by replacing x with 3 and y with 125 in each equation.

Example 3 Write and Solve a System of Equations Checky =35x + 20y =25x + 50 Answer:The solution means that in week 3, Naresh and Diego will have ridden the same number of miles, =35(3) =25(3) = =125

Example 3 A.225 weeks B.7 weeks C.5 weeks D.20 weeks Alex and Amber are both saving money for a summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money?