Chapter 2 Lesson 3 Systems of Linear Equations in Two Variables.

Slides:

Advertisements

Similar presentations

3.2 Solving Systems Algebraically 2. Solving Systems by Elimination.

Advertisements

Solving Systems of Equations

Topic: Solving Systems of Linear Equations Algebraically.

5.3 Solving Systems using Elimination

Systems of Linear Equations Math 0099 Section Section Created and Presented by Laura Ralston.

Section 11.2 Systems of Linear Equations

7.1 Graphing Linear Systems

Systems of Linear Equations

Solving Systems of Equations: Elimination Method.

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

Unit 1.3 USE YOUR CALCULATOR!!!.

Chapter 2 Systems of Linear Equations and Matrices Section 2.1 Solutions of Linear Systems.

Section 3.5 Systems of Equations. What is a system of equations? Two or more equations in the same variables.

Section 10.1 Systems of Linear Equations; Substitution and Elimination 1.

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.

SYSTEMS OF LINEAR EQUATIONS SUBSTITUTION AND ELIMINATION Objectives: Solve Systems of Equations by Substitution and Elimination Identify Inconsistent Systems.

Solving Systems of Equations Algebraically Chapter 3.2.

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 3.2, Slide 1 Chapter 3 Systems of Linear Equations.

By looking at a graph, name the three types of solutions that you can have in a system of equations. Groupwork graded Groupwork worksheet 1-14 Work on.

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.

3-2 Solving Linear Systems Algebraically Objective: CA 2.0: Students solve system of linear equations in two variables algebraically.

Chapter 8 Section 3 Solving System of Equations by the Addition Method.

Notes – 2/13 Addition Method of solving a System of Equations Also called the Elimination Method.

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using.

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

Chapter 4 Section 4.1 Solving Systems of Equations in Two Variables.

Section 4.1 Systems of Linear Equations in Two Variables.

Warm-up 4-1. x – y = 33x + y = 52y = 6 – x x + y = 5x – 2y = 43x – 2y = 6 Graphs:

Solving a System of Equations in Two Variables By Graphing Chapter 8.1.

Good Morning, We are moving on to chapter 3. If there is time today I will show you your test score you can not have them back as I still have several.

Solve by Graphing Solve: 3x + 4y = - 4 x + 2y = 2

MAT 150 Module 10 – Systems of Equations Lesson 1 – Systems of Linear Equations.

Systems of equations 2 or more equations on the same graph.

Wednesday: Factoring Warm-up Find the factors and solutions.

Solving Systems of Equations

Introduction to Systems of Equations (and Solving by Graphing) Unit 5 Day 3.

Slide Copyright © 2009 Pearson Education, Inc. 7.2 Solving Systems of Equations by the Substitution and Addition Methods.

3-2 Solving Systems Algebraically. In addition to graphing, which we looked at earlier, we will explore two other methods of solving systems of equations.

Tuesday, October 15, 2013 Do Now:. 3-1 Solving Systems of Equations by Graphing Objectives: 1)solve systems of linear equations by graphing 2) Determine.

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

Systems of Equations. OBJECTIVES To understand what a system of equations is. Be able to solve a system of equations from graphing, substitution, or elimination.

Task 2.6 Solving Systems of Equations. Solving Systems using Substitution  Solve using Substitution if one variable is isolated!!!  Substitute the isolated.

3.2 Solve Linear Systems Algebraically Algebra II.

 Students will be able to solve linear systems using substitution. In Chapter 3-1, you were able to solve a linear system of equations by rewriting each.

Chapter 5: Systems of Linear Equations Section 5.1: Solving Systems of Linear Equations by Elimination.

Solving Systems of Linear Equations in 2 Variables Section 4.1.

6) x + 2y = 2 x – 4y = 14.

Solve by Graphing Solve: 3x + 4y = - 4 x + 2y = 2

Systems of Equations An Introduction.

10.1 SYSTEMS OF LINEAR EQUATIONS: SUBTRACTION, ELIMINATION.

ALGEBRA 1 CHAPTER 7 LESSON 5 SOLVE SPECIAL TYPES OF LINEAR SYSTEMS.

Solve Systems of Equations by Elimination

Systems of Linear Equations

Solving Systems of Linear Equations

Solving Systems Using Elimination

MATRICES AND DETERMINANTS

Break even or intersection

Objective The student will be able to: solve systems of equations using elimination with multiplication.

Introduction to Systems of Equations (and Solving by Graphing)

Lesson 7.1 How do you solve systems of linear equations by graphing?

Solve Linear Equations by Elimination

Before: December 4, 2017 Solve each system by substitution. Steps:

SYSTEMS OF LINEAR EQUATIONS

Systems of linear equations substitution and elimination

Systems of Equations Solve by Graphing.

7.1 Solving Systems of Equations

Lesson 0 – 8 Systems of Linear Equations

Nonlinear Systems of Equations

Chapter 5 Review.

Systems of three equations with three variables are often called 3-by-3 systems. In general, to find a single solution to any system of equations,

Presentation transcript:

Chapter 2 Lesson 3 Systems of Linear Equations in Two Variables

Different methods of solving System of Equations in Two Variables  Graphically/Intersection  Substitution  Elimination

Solving a System of Equations Graphically  Get both equations into slope-intercept form  Y=mx+b  Graph both equations on your calculator  Y= menu  First equation in Y1  Second equation in Y2  Find their intersection  2 nd Trace  Option 5:intersection  Press ENTER 3 times  List X and Y values as an ordered pair

Examples

Solving System of Equations by Substitution  In one of the equations, solve for one of the variables  Doesn’t matter which one, pick whichever is easier  Substitute what that variable equals into the second equation for that variable  Has to be other equation, cannot use same equation  Solve for the remaining variable  Pick an equation to substitute the variable you solved for, solve for the other variable.  Doesn’t matter which equation, pick the easier one.

Examples

Solving a System of Equations by Elimination  Multiply one or both of the equations by a constant so that one of the variables has the same coefficient in both equations.  If the sign in front of the coefficient is the same in both equations, subtract one equation from the other.  If the sign in front of the coefficient is different in both equations, add the equations together.  Solve for the remaining variable.  In one of the equations, substitute the value in for the variable you solved for, then solve for the remaining variable.

Examples

Dependent and Inconsistent Systems  A system of equations has 3 possible outcomes.  1)The two equations will intersect at one point and have a unique solution.  2)The two equations will graph the same line resulting in an infinite number of solutions, this is called a dependent system.  3)The two equations are parallel and will never intersect, resulting in no solution, this is called an inconsistent system.

Examples

Homework  Page  1,3,6,9,11,13,15,17,19,21,23,26,31,33,37,38,41,43, 47,49,53,57,63,65