3-1 Graphing Systems of Equations

Slides:

Advertisements

Similar presentations

Solving Special Systems

Advertisements

Unit 4 – Linear Systems in Two Dimensions Topic: Solving Linear Systems of Equations.

Solving Systems of Equations and Inequalities Jeopardy

UNIT 6.15 Special Solutions: Graphing I can identify special solutions within a system of equations graphically.

Solving System of Equations Using Graphing

7.1 Graphing Linear Systems

Solving Systems of Linear Equations by Graphing

Solving Systems of Linear Equations Graphically

Solving Special Systems

Topic: Solving Systems of Linear Equations by Graphing.

You will need: -Spiral/paper to take notes -A textbook (in this corner =>) -The Pre-AP agreement if you have it signed.

3.1 WARM-UP Graph each of the following problems

Holt McDougal Algebra Solving Special Systems Warm Up Solve each equation. 1. 2x + 3 = 2x (x + 1) = 2x + 2 no solution infinitely many solutions.

Linear Systems of Equations Section 3.1. What is a “system” of equations?

What is a system of equations? A system of equations is when you have two or more equations using the same variables. The solution to the system is the.

Warm Up 1.) Find the x – intercept of the graph of y = |x + 1|. 2.) Express the cost C of x ball game tickets at a price of $18 per ticket.

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.

Objectives Solve special systems of linear equations in two variables.

Holt Algebra Solving Special Systems 6-4 Solving Special Systems Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.

Objective The student will be able to: solve systems of equations by graphing.

3.1 Solve Linear Systems by Graphing Algebra II. Definition A system of two linear equations in two variables x and y, also called a linear system, consists.

Holt Algebra Solving Special Systems 6-4 Solving Special Systems Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.

3.1 Graphing Systems of Equations The superior man is modest in his speech, but exceeds in his actions.

REVIEW OF 3-1 AND 3-2 A) Solve by graphing y = 2x – 1 y = -3/4x + 10

Lesson 4-1 Solving linear system of equations by graphing

3.1 Graphing Systems of Equations

Classifying Systems, Solving Systems by Graphing and Substitution

10.1 SYSTEMS OF LINEAR EQUATIONS: SUBTRACTION, ELIMINATION.

Solving Special Systems

Solving Special Systems

Objectives Graph lines and write their equations in slope-intercept form. Classify lines as parallel, intersecting, or coinciding.

Solving Special Systems

Five-Minute Check (over Lesson 1-5) Mathematical Practices Then/Now

Solving Special Systems

Systems of Linear Equations

5.1 Graphing Systems of Equations

Warm - Up Graph: 4x – 3y = 9.

6-1 Solving Systems by Graphing

Warm-Up 1. Determine the mistake. Then correctly solve. 4x +6 = -3(x+ 4) step 1 4x +6 = -3x – 12 step 2 x +6 = -12 step 3 x = -18 step 4 2. Determine the.

Solve Systems of Equations

Solving Special Systems

Do Now 1/18/12 In your notebook, explain how you know if two equations contain one solution, no solutions, or infinitely many solutions. Provide an example.

Warm-Up What do you have to do to make this problem solvable?

Solving Special Systems

infinitely many solutions

Solving Special Systems

Lesson Objectives: I will be able to …

Solving Special Systems

Systems of Linear Equations and Problem Solving

Solving Special Systems

Solving Systems of Linear and Quadratic Equations

Using Graphs and Tables to Solve Linear Systems 3-1

Systems of Equations.

Objectives Identify solutions of linear equations in two variables.

Chapter 8 Systems of Equations 8.1 Solve Systems by Graphing

Solving Special Systems

Solving Special Systems

Systems of Equations Solving by Graphing.

Solving Special Systems

Algebra 1 Section 7.5.

1.2 Solving Linear Systems by Graphing

3.1 Graphing Systems of Equations

Solving Special Systems

Objectives Graph lines and write their equations in slope-intercept form. Classify lines as parallel, intersecting, or coinciding.

Solving Special Systems

Solving Special Systems

Solving Special Systems

Solving Linear Systems by Graphing

Presentation transcript:

3-1 Graphing Systems of Equations M11.D.2.1.4: Write and/or solve systems of equations using graphing, substitution and/or elimination

Objectives Systems of Linear Equations

Vocabulary A system of equations is a set of two or more equations that use the same variables. If the graph of each equation in a system of two variables is a line, then the system is a linear system.

Solving by Graphing Solve the system by graphing. x + 3y = 2 Graph the equations and find the intersection. The solution appears to be (–4, 2). x + 3y = 2 3x + 3y = –6 Check: Show that (–4, 2) makes both equations true. x + 3y = 2 3x + 3y = –6 (–4) + 3(2) 2 3(–4) + 3(2) –6 (–4) + 6 2 –12 + 6 –6 2 = 2 –6 = –6

Real World Example The table shows the number of pairs of shoes sold by two new employees at a shoe store. Find linear models for each employee’s sales. Graph the data and models. Predict the week in which they could sell the same number of pairs of shoes. Week 1 2 3 4 Ed 50 55 63 67 Jo 40 47 56 62 Step 1: Let x = number of weeks. Let y = number of shoes sold. Use the LinReg feature of the graphing calculator to find linear models. Rounded versions appear below. Ed’s rate: y = 5.9x + 44 Jo’s rate: y = 7.5x + 32.5

Continued Step 2: Graph each model. Use the intersect feature. The two lines meet at about (7.2, 86.4). If the trends continue, the number of pairs of shoes that Ed and Jo will sell will be equal in about week 7.

Graphical Solutions of Linear Systems in Two Variables Vocabulary Graphical Solutions of Linear Systems in Two Variables Intersecting Lines Coinciding Lines Parallel Lines One Solution Independent No Unique Solution Dependent No Solution Inconsistent

Classifying the System Classify the system without graphing. y = 3x + 2 –6x + 2y = 4 y = 3x + 2 –6x + 2y = 4 Rewrite in slope-intercept form. y = 3x + 2 m = 3, b = 2 Find the slope and y-intercept. m = 3, b = 2 Since the slopes are the same, the lines could be the same or coinciding. Compare the y-intercepts. Since the y-intercepts are the same, the lines coincide. It is a dependent system.

Homework Pg 120 & 121 # 1,2,10,13,14,16