3.2 Solving Linear Systems Algebraically

Slides:

Advertisements

Similar presentations

September 11, 2014 Page 18 – 19 in Notes

Advertisements

3.2 Solving Systems Algebraically 2. Solving Systems by Elimination.

Elimination Using Multiplication.

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.

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.

5.3 Solving Systems of Linear Equations by the Addition Method

Solving Systems of Equations: Elimination Method.

5.1 Solving Systems of Linear Equations by Graphing

Systems of Linear Equations Solving 2 Equations. Review of an Equation & It’s Solution Algebra is primarily about solving for variables. The value or.

Solving Linear Systems using Linear Combinations (Addition Method) Goal: To solve a system of linear equations using linear combinations.

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,

Algebra 2 Chapter 3 Notes Systems of Linear Equalities and Inequalities Algebra 2 Chapter 3 Notes Systems of Linear Equalities and Inequalities.

Unit 1.3 USE YOUR CALCULATOR!!!.

Solving Systems of Equations

8.1 Solving Systems of Linear Equations by Graphing

Warm-up Twice the supplement of an angle is ten times the measure of the angle itself. Find the measure of both angles. Three times the complement of an.

Goal: Solve systems of linear equations using elimination. Eligible Content: A / A

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

Warm Up 12/5 1) Is (-2, 3) a solution? 3x + y = -3 3x + y = -3 2x – 4y = 6 2x – 4y = 6 2) Find the solution by graphing y = -4 + x x + y = 6 3) Solve:

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

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

6-2B Solving by Linear Combinations Warm-up (IN) Learning Objective: to solve systems of equations using linear combinations. Solve the systems using substitution.

What is a System of Linear Equations? A system of linear equations is simply two or more linear equations using the same variables. We will only be dealing.

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.

Elimination Method: Solve the linear system. -8x + 3y=12 8x - 9y=12.

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

Lesson 7.4A Solving Linear Systems Using Elimination.

SECONDARY ONE 6.1a Using Substitution to Solve a System.

6.2 Solve a System by Using Linear Combinations

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

SYSTEMS OF EQUATIONS. SYSTEM OF EQUATIONS -Two or more linear equations involving the same variable.

Quiz next Friday, March 20 th Sections 1-0 to minutes – at the beginning of class.

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

3.3 Solving Linear Systems by Linear Combination 10/12/12.

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

Ch. 7 – Matrices and Systems of Equations Elimination.

3.2 Solve Linear Systems Algebraically Algebra II.

Solving Systems of Linear Equations in 2 Variables Section 4.1.

SECTION 3.2 SOLVING LINEAR SYSTEMS ALGEBRAICALLY Advanced Algebra Notes.

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.

Elimination Week 17 blog post. Add or subtract In elimination, we have to add or subtract two linear equations to isolate one of the variables. So, the.

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.

Warm Up Find the solution to linear system using the substitution method. 1) 2x = 82) x = 3y - 11 x + y = 2 2x – 5y = 33 x + y = 2 2x – 5y = 33.

Systems of Equations Draw 2 lines on a piece of paper. There are three possible outcomes.

6) x + 2y = 2 x – 4y = 14.

5.3 Elimination Using Addition and Subtraction

3.2 Solving Systems by Elimination

Solving Systems of Linear Equations in 3 Variables.

Solving Linear Systems by Linear Combinations

3.2 Solve Linear Systems Algebraically

THE SUBSTITUTION METHOD

SYSTEMS OF LINEAR EQUATIONS

Solving Linear Systems Algebraically

REVIEW: Solving Linear Systems by Elimination

Solve Systems of Equations by Elimination

3.5 Solving systems of equations in 3 variables

Solve Linear Equations by Elimination

3.4 Solving Systems of Linear Equations in 3 Variables

Solving Linear Systems by Linear Combinations (Elimination)

SYSTEMS OF LINEAR EQUATIONS

Solving Systems of Linear Equations in 3 Variables.

Section Solving Linear Systems Algebraically

Solve the linear system.

Example 2B: Solving Linear Systems by Elimination

6-3 & 6-4 Solving Systems by Elimination

Solving Linear Systems by Graphing

Presentation transcript:

3.2 Solving Linear Systems Algebraically Algebra II

2 Methods for Solving Algebraically Substitution Method (used mostly when one of the equations has a variable with a coefficient of 1 or -1) Linear Combination Method or Elimination Method (use any time)

Substitution Method Solve one of the given equations for one of the variables with a coefficient of 1 or -1. Substitute the expression from step 1 into the other equation and solve for the remaining variable. Substitute the value from step 2 into the revised equation from step 1 and solve for the 2nd variable. Write the solution as an ordered pair (x,y).

Ex. 1: Solve using sub. method Now, solve for x. 2x+6x-26= -10 8x=16 x=2 Now substitute the 2 in for x in for the equation from step 1. y=3(2)-13 y=6-13 y=-7 Solution: (2,-7) Plug in to check soln. 3x-y=13 2x+2y= -10 Solve the 1st eqn for y. -y= -3x+13 y=3x-13 Now substitute 3x-13 in for the y in the 2nd equation. 2x+2(3x-13)= -10

3-2B Solving linear Systems using the elimination method

Linear Combination or Elimination Method Multiply one or both equations by a real number so that when the equations are added together one variable will cancel out. Add the 2 equations together. Solve for the remaining variable. Substitute the value from step 2 into one of the original equations and solve for the other variable. Write the solution as an ordered pair (x,y).

Ex. 1: Solve using lin. combo. (elimination) method. 2x-6y=19 -3x+2y=10 Multiply the entire 2nd eqn. by 3. 2x-6y=19 2x– 6y=19 3(-3x+2y=10) -9x+6y=30 -7x=49 2. Now add the 2 eq.’s together and solve for the variable. x=-7 Substitute the -7 in for x in one of the original equations. 2(-7)-6y=19 -14-6y=19 -6y=33 y= -11/2 Now write as an ordered pair. (-7, -5½ ) Plug into both equations to check.

Means any point on the line is a solution. Ex. 2: Choose a method. 9x-3y=15 -3x+y= -5 Which method? Substitution! Solve 2nd eqn for y. y=3x-5 9x-3(3x-5)=15 9x-9x+15=15 15=15 OK, so? What does this mean? Both equations are for the same line! many solutions Means any point on the line is a solution.

Ex. 3: Solve using either method. 6x-4y=14 -3x+2y=7 Which method? Linear combo! Multiply 2nd eqn by 2. +-6x+4y=14 0=28 Huh? What does this mean? It means the 2 lines are parallel. No solution Since the lines do not intersect, they have no points in common.

Assignment