3-2 Solving Systems Algebraically (p. 125) Algebra 2 Prentice Hall, 2007.

Slides:

Advertisements

Similar presentations

SYSTEMS OF LINEAR EQUATIONS

Advertisements

Solving Systems of three equations with three variables Using substitution or elimination.

Part 2.  Review…  Solve the following system by elimination:  x + 2y = 1 5x – 4y = -23  (2)x + (2)2y = 2(1)  2x + 4y = 2 5x – 4y = -23  7x = -21.

4.3 Systems of Equations - Elimination Objective: The student will be able to: Solve systems of equations using elimination with addition and subtraction.

3.5 Solving systems of equations in 3 variables

Algebra II w/ trig. Substitution Method: 1. Solve an equation for x or y 2. Substitute your result from step 1 into the other equation and solve for the.

Elimination Using Addition and Subtraction. Solving Systems of Equations So far, we have solved systems using graphing and substitution. Solve the system.

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

Solving Systems of Equations: Elimination Method.

ALGEBRA II SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS.

Solving Systems of Equations

3.5 Solving Systems of Equations in Three Variables The student will be able to solve systems of linear equations in three variables algebraically.

Algebra-2 Section 3-2A Solving Systems of Linear Equations Algebraically Using Substitution.

Solving Linear Systems by Substitution O Chapter 7 Section 2.

Solving Systems Using Elimination

Section 3-2: Solving Systems Algebraically (Pg.125) By Ms. Beydoun.

Textbook Section 6-2.  Students can solve a system of equations using substitution.  Students can classify systems as consistent, inconsistent, dependent,

3.2 Solving Linear Systems Algebraically p Methods for Solving Algebraically 1.Substitution Method (used mostly when one of the equations has.

5.2: Solving Systems of Equations using Substitution

Solving by Substitution Method or Elimination (Addition) Method

3.2 Solving Linear Systems Algebraically Honors. 2 Methods for Solving Algebraically 1.Substitution Method (used mostly when one of the equations has.

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

Do Now (3x + y) – (2x + y) 4(2x + 3y) – (8x – y)

Systems of Linear Equations in Two Variables. 1. Determine whether the given ordered pair is a solution of the system.

Solving Systems of Linear Equations by Substitution; Applications Solve systems of linear equations using substitution. 2.Solve applications involving.

Advanced Algebra Notes Section 3.4: Solve Systems of Linear Equations in Three Variables A ___________________________ x, y, and z is an equation of the.

Chapter 3 Examples Section 5 Solving System of Equations Algebraically with 3 variables.

U SING A LGEBRAIC M ETHODS TO S OLVE S YSTEMS In this lesson you will study two algebraic methods for solving linear systems. The first method is called.

Solving Linear Systems by Substitution

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

SOLVING SYSTEMS USING ELIMINATION 6-3. Solve the linear system using elimination. 5x – 6y = -32 3x + 6y = 48 (2, 7)

3.2 Solving Linear Systems Algebraically What are the steps to solve a system by substitution? What clue will you see to know if substitution is a good.

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.

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

Solving systems of equations with three variables January 13, 2010.

System of Equations Solve by Substitution. A System of Equations:  Consists of two linear equations  We want to find out information about the two lines:

Lesson 4-2: Solving Systems – Substitution & Linear Combinations Objectives: Students will: Solve systems of equations using substitution and linear combinations.

Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:

OBJ: Solve Linear systems graphically & algebraically Do Now: Solve GRAPHICALLY 1) y = 2x – 4 y = x - 1 Do Now: Solve ALGEBRAICALLY *Substitution OR Linear.

3.2 Solve Linear Systems Algebraically Algebra II.

Mrs. Manley Systems of Equations How do you find solutions to systems of two linear equations in 2 variables?

Elimination Method - Systems. Elimination Method  With the elimination method, you create like terms that add to zero.

Warm-Up Solve the system by graphing y = x + 2 x = −3 Solve the system by graphing 4x + y = 2 x − y = 3.

Solve linear systems by substitution.

Algebra 1 Review Systems of Linear Equations Using Substitution

6) x + 2y = 2 x – 4y = 14.

Objective I can solve systems of equations using elimination with addition and subtraction.

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

The student will be able to:

THE SUBSTITUTION METHOD

6-2 Solving Systems using Substitution

Solving Linear Systems Algebraically

3.5 Solving systems of equations in 3 variables

ALGEBRA REVIEW PROBLEMS

Solving Systems of Equations using Substitution

Systems of Linear Equations in Two Variables

Lesson Objectives: I will be able to …

There are infinite solutions to the system.

SYSTEMS OF LINEAR EQUATIONS

Systems with Three Variables

Section Solving Linear Systems Algebraically

6.2 Using Substitution to Solve Systems

Chapter 9 Lesson 4 Solve Linear Systems By Substitution

SOLVING SYSTEMS OF EQUATIONS.

The student will be able to:

6-3 & 6-4 Elimination Goals: Solve systems using linear combinations.

The student will be able to:

SOLVING SYSTEMS OF EQUATIONS.

SOLVING SYSTEMS OF EQUATIONS.

Presentation transcript:

3-2 Solving Systems Algebraically (p. 125) Algebra 2 Prentice Hall, 2007

Content Objectives You will… Solve a system of linear equations using the process of SUBSTITUTION. Solve a system of linear equations using the process of ELIMINATION. Be able to decide which method would be the easiest to use.

Substitution Method 1.Choose 1 equation and solve for the “easiest” variable. 2.Substitute that “expression” into the other equation for the variable it represents. 3.Solve for the 2nd variable. 4.Substitute the value of that variable into 1 of the 2 original equations to find the value of the 1st variable.

Example Solve the system using substitution: Hint: Solve for y in the 1st equation.

Example Solve the system using substitution: Hint: Solve for x in either equation.

Elimination Method 1.Write both equations in Standard Form. 2.“Doctor-up” 1 or both equations so that the x’s OR y’s are zero pairs. 3.Combine the 2 equations, thereby eliminating one of the variables. 4.Solve for the remaining variable. 5.Substitute the value of that variable into either of the original equations to find the other variable.

Example Solve the system using elimination: Hint: Doctor-up one equation in order to eliminate x.

Example Solve the system using elimination: Hint: Doctor-up both equations in order to eliminate x OR y... Your choice!

Example Solve the system using whichever method you want: No Solution!

What if…? … both variables get eliminated and you end up with a false statement? NO Solution … both variables get eliminated and you end up with a true statement? Infinite # of Solutions

Homework 3-2 p. 128: m.o.5 (5-50)