Ants, Freeways, & Other Systems. Solving linear Systems Algebraically State Standard – 2.0 Students solve systems of linear equations and.

Slides:

Advertisements

Similar presentations

Solving Linear Systems by Linear Combinations

Advertisements

Chapter 3: Systems of Linear Equations and Inequalities.

+ Water wars An enemy submarine has launched a missile toward another submarine in your fleet following the path 2x-y=4. Your submarine retaliates launching.

3-6 Solving Systems of Linear Equations in Three Variables Objective: CA 2.0: Students solve systems of linear equations and inequalities in three variables.

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.

Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using.

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.

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

7.1 SOLVING SYSTEMS BY GRAPHING The students will be able to: Identify solutions of linear equations in two variables. Solve systems of linear equations.

Solving Linear Systems by Linear Combinations

ALGEBRA II SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS.

3.2 Solving Systems Algebraically

Unit 1.3 USE YOUR CALCULATOR!!!.

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

Do Now 1/13/12  In your notebook, list the possible ways to solve a linear system. Then solve the following systems. 5x + 6y = 50 -x + 6y = 26 -8y + 6x.

Integrated Math 2 Lesson #7 Systems of Equations - Elimination Mrs. Goodman.

Objective I will identify the number of solutions a linear system has using one of the three methods used for solving linear systems.

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

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.

Warm-Up Exercises Solve the system by substitution. 2x2x y = – 1. 3x3x – y – = 1 4x+y = 2. 72x2x+3y3y = – ANSWER () 1, 2 – ANSWER () 1, 3.

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

Solving by Substitution Method or Elimination (Addition) Method

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.

7.4. 5x + 2y = 16 5x + 2y = 16 3x – 4y = 20 3x – 4y = 20 In this linear system neither variable can be eliminated by adding the equations. In this linear.

Unit 1.3 USE YOUR CALCULATOR!!! MM3A5c. Unit 1 – Algebra: Linear Systems, Matrices, & Vertex- Edge Graphs  1.3 – Solve Linear Systems Algebraically 

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

SystemsOfInequalities. 7-1 Solving Systems by Graphing What is a system of linear equations? “SOLUTION” No solution Infinitely Many Solutions Page 342.

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

Solving Systems of Equations by Elimination. Standard and Objective A.REI.5 Prove that, given a system of two equations in two variables, replacing one.

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

EXAMPLE 4 Solve linear systems with many or no solutions Solve the linear system. a.x – 2y = 4 3x – 6y = 8 b.4x – 10y = 8 – 14x + 35y = – 28 SOLUTION a.

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

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

3.2 Solve Linear Systems Algebraically Algebra II.

Chapter 3 Section 2. EXAMPLE 1 Use the substitution method Solve the system using the substitution method. 2x + 5y = –5 x + 3y = 3 Equation 1 Equation.

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

Solving Linear Systems Using Substitution There are two methods of solving a system of equations algebraically: Elimination Substitution - usually used.

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.

Ch. 3 Notes 3.1 – 3.3 and 3.6.

Use the elimination method

Algebra 2 Chapter 3 Review Sections: 3-1, 3-2 part 1 & 2, 3-3, and 3-5.

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.

3.2 WARM - UP Solve the system graphically. 4x – 2y = -8 x + y = 1 –5–4–3–2– –5 –4 –3 –2 – x – 2y = -8 -4x -2y = -4x – 8 y = 2x + 4 x.

Objective: Students will solve multistep equations using the property of opposites and combining like terms Standard: 4.0 Students simplify expressions.

6) x + 2y = 2 x – 4y = 14.

10.3 Solving Linear Systems

Solving Systems of Equations by Elimination2

Solving Systems of Linear Equations in 3 Variables.

Chapter 3: Linear Systems

THE SUBSTITUTION METHOD

Use ELIMINATION (also known as LINEAR COMBINATIONS) !!

Solving Linear Systems by Linear Combinations

Solving Linear Systems Algebraically

Solve a system of linear equation in two variables

3.5 Solving systems of equations in 3 variables

Solve Systems of Linear Equations in Three Variables

7.4 Solve Linear Systems by Multiplying First

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

Solve Linear Equations by Elimination

Solving Systems of Linear Equations in 3 Variables.

Systems of Equations Solve by Graphing.

Section Solving Linear Systems Algebraically

Solve the linear system.

Example 2B: Solving Linear Systems by Elimination

Algebra 2 Monday, October 20, 2014

Warm-Up # Is (–1, 4) a solution to

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:

Ants, Freeways, & Other Systems

Solving linear Systems Algebraically State Standard – 2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, linear combination, with graphs, or with matrices. Created by Jason L. Bradbury The Linear Combination Method 1) Multiply one or both of the equations by a constant. 2) Add the revised equations in order to eliminate one of the variables. 3) Substitute the value in Step 2 into one of the original equations to get the other variable

(, ) Example 1 Solve using the Linear Combination method: 2x – 4y = 13 4x – 5y = 8 -2( )2x – 4y = 13 4x – 5y = 8 -4x + 8y = -26 4x – 5y = 8 3y = -18 y = -6 2x – 4(-6) = 13 2x + 24 = x = -11 x =

(, ) Example 2 Solve using the Linear Combination method: 2x + 3y = -1 -5x + 5y = 15 5( )2x + 3y = -1 -5x + 5y = 15 10x + 15y = x + 10y = 30 25y = 25 y = 1 2x + 3(1) = -1 2x + 3 = x = -4 x = ( )

Example 3 A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make? -2( )14p + 6s = 64 39p + 12s = p – 12s = p + 12s = p = 22 p = 2 14(2)+ 6s = s = s = 36 s = 6 The caterer should make 2 pans of pasta and 6 trays of sandwiches.

Guided Practice 6x + 6y = 3 4x + 4y = 2 3x – 3y = 3 -4x + y = 21 -2x + y = 13 x – 4y = -31 x – 6y = 6 -3x + 2y = -2 -5x + 7y = 10 15x – 21y = 22 -4x + 8y = 24 -x + 2y = 6

If you get the variables to cancel and you get: 0 = 0 You will have: Infinitely many solutions No solutions If you get the variables to cancel and you get: 0 = (some #) You will have:

HOMEWORK Due Tomorrow:Worksheet