Example 1 Solution by Elimination Chapter 7.1 Solve the system  2009 PBLPathways.

Slides:

Advertisements

Similar presentations

Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

Advertisements

Triangular Form and Gaussian Elimination Boldly on to Sec. 7.3a…

Directions: Solve the linear systems of equations by graphing. Use the graph paper from the table. Tell whether you think the problems have one solution,

Objectives  Solve systems of linear equations in three variables using left-to-right elimination  Find solutions of dependent systems  Determine when.

Adapted from Walch Education Proving Equivalencies.

Solve each with substitution. 2x+y = 6 y = -3x+5 3x+4y=4 y=-3x- 3

Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.

Bell Work2/12/15 Solve the system by elimination..

© 2007 by S - Squared, Inc. All Rights Reserved.

Solving Systems of Linear Equations

Graphing Systems of Equations Graph of a System Intersecting lines- intersect at one point One solution Same Line- always are on top of each other,

SECTION 6.1 SYSTEMS OF LINEAR EQUATIONS: SYSTEMS OF LINEAR EQUATIONS: SUBSTITUTION AND ELIMINATION SUBSTITUTION AND ELIMINATION.

Objectives  Solve systems of linear equations in three variables using left-to-right elimination  Find solutions of dependent systems  Determine when.

Example 2 Combining Graphical and Algebraic Methods Chapter 6.4 Solve the equation.

Goal: Solve a system of linear equations in two variables by the linear combination method.

Solving a System of Equations in Two Variables By Elimination Chapter 8.3.

Triangular Form and Gaussian Elimination Boldly on to Sec. 7.3a… HW: p odd.

SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.

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

Example 3 Finding an Inverse Function Chapter 4.3 a.Find the inverse function of. b.Graph and its inverse function on the same axes.  2009 PBLPathways.

Chapter 2.2 The Multiplication Principle of Equality.

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

Multiply one equation, then add

© 2007 by S - Squared, Inc. All Rights Reserved.

Multi Step Equations. Algebra Examples 3/8 – 1/4x = 1/2x – 3/4 3/8 – 1/4x = 1/2x – 3/4 8(3/8 – 1/4x) = 8(1/2x – 3/4) (Multiply both sides by 8) 8(3/8.

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

Example 1 Solving a Nonlinear System Algebraically Chapter 7.5 Use substitution to solve the system and check the solution.  2009 PBLPathways.

Elimination using Multiplication Honors Math – Grade 8.

Solving 2 step equations. Two step equations have addition or subtraction and multiply or divide 3x + 1 = 10 3x + 1 = 10 4y + 2 = 10 4y + 2 = 10 2b +

5.4 Elimination Using Multiplication Algebra 1 Objective: Each student will understand if addition and subtraction does not eliminate a variable – how.

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

WARM-UP. SYSTEMS OF EQUATIONS: ELIMINATION 1)Rewrite each equation in standard form, eliminating fraction coefficients. 2)If necessary, multiply one.

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

Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.

Solve Linear Systems By Multiplying First

3. 3 Solving Equations Using Addition or Subtraction 3

Example: Solve the equation. Multiply both sides by 5. Simplify both sides. Add –3y to both sides. Simplify both sides. Add –30 to both sides. Simplify.

Objective I CAN solve systems of equations using elimination with multiplication.

Solve Systems of Equations by Elimination

Solving Systems of Linear Equations in 3 Variables.

Solving Two-Step Equations

Equations with variables on both sides Whiteboard practice

Solve for variable 3x = 6 7x = -21

Solve an equation by multiplying by a reciprocal

3.1 Solving Two-Step Equations

Solving Equations: The Multiplication Principle

Warm Up Simplify each expression. 1. 3x + 2y – 5x – 2y

6-2 Solving Systems Using Substitution

Solving Systems of Equations

Solving One-Step Equations

6-3 Solving Systems Using Elimination

REVIEW: Solving Linear Systems by Elimination

Solve Systems of Equations by Elimination

Solve Linear Equations by Elimination

Objectives Solve systems of linear equations in two variables by elimination. Compare and choose an appropriate method for solving systems of linear equations.

Solving one- and two-step equations

SIMULTANEOUS EQUATIONS 1

Equations with variables on both sides Whiteboard practice

a + 2 = 6 What does this represent? 2 a

Solving a System of Equations in Two Variables by the Addition Method

Subtract the same value on each side

Solving Systems of Linear Equations in 3 Variables.

Systems of Equations Solve by Graphing.

Equations …. are mathematical sentences stating that two expressions are equivalent.

6.3 Using Elimination to Solve Systems

Learn to solve 2-step equations

Example 2B: Solving Linear Systems by Elimination

3.1 Solving Two-Step Equations 1 3x + 7 = –5 3x + 7 = –5 – 7 – 7

The Substitution Method

Presentation transcript:

example 1 Solution by Elimination Chapter 7.1 Solve the system  2009 PBLPathways

Solve the system

 2009 PBLPathways Solve the system 1.If necessary, interchange two equations or use multiplication to make the coefficient of x in the first equation a 1. E1  E2

 2009 PBLPathways Solve the system 2.Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become R1 + R2  R2

 2009 PBLPathways Solve the system 2.Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become E1 + E2  E2

 2009 PBLPathways Solve the system 2.Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become E1 + E2  E2

 2009 PBLPathways Solve the system 2.Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become R1 + R3  R3

 2009 PBLPathways Solve the system 2.Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become E1 + E3  E3

 2009 PBLPathways Solve the system 2.Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become E1 + E3  E3

 2009 PBLPathways Solve the system 2.Add a multiple of the first equation to each of the following equations so that the coefficients of x in the second and third equations become E1 + E3  E3

 2009 PBLPathways Solve the system 3.Multiply (or divide) both sides of the second equation by a number that makes the coefficient of y in the second equation equal to R2  R2

 2009 PBLPathways Solve the system 3.Multiply (or divide) both sides of the second equation by a number that makes the coefficient of y in the second equation equal to E2  E2

 2009 PBLPathways Solve the system 3.Multiply (or divide) both sides of the second equation by a number that makes the coefficient of y in the second equation equal to E2  E2

 2009 PBLPathways Solve the system 4.Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes R2 + R3  R3

 2009 PBLPathways Solve the system 4.Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes E2 + E3  E3

 2009 PBLPathways Solve the system 4.Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes E2 + E3  E3

 2009 PBLPathways Solve the system 4.Add a multiple of the (new) second equation to the (new) third equation so that the coefficient of y in the newest third equation becomes E2 + E3  E3

 2009 PBLPathways Solve the system 5.Multiply (or divide) both sides of the third equation by a number that makes the coefficient of z in the third equation equal to 1. This gives the solution for z in the system of equations. E3  E3

 2009 PBLPathways Solve the system 5.Multiply (or divide) both sides of the third equation by a number that makes the coefficient of z in the third equation equal to 1. This gives the solution for z in the system of equations. E3  E3

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Solve the system 6.Use the solution for z to solve for y in the second equation. Then substitute values for y and z to solve for x in the first equation.

 2009 PBLPathways Does the solution solve the system? Solve the system