Lesson System of Equations (Elimination Method)

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1 Lesson: Lesson System of Equations (Elimination Method) Supplement System of Equations (Elimination Method) Teacher Lesson Plan CC Standards 8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. 8.EE.C.8a (Calculator No) Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8.EE.C.8b (Calculator No) Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 8.EE.C.8c (Calculator Yes) Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair Calculator Teacher call, but I would lean towards yes on this lesson. Most of the lesson pertains to 8.EE.8c. Objective The students will practice solving system of equations using the elimination method. Mathematical Practices #1 Make sense of problems and persevere in solving them. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make sense of structure. Teacher Input Bellwork: Homework: Introduction: Lesson: Review bellwork. Review previous night s homework. Introduce the lesson as directed by PowerPoint. Teach as directed by the PowerPoint. Students notes coincide with the lesson. Extra Practice Classwork Page 4 Extra Practice Page 5 (can be used for homework or extra practice) Closure Teacher selected 1 P a g e

SECTION 1: Warm-up Activity Lesson 5.2.4 System of Equations (Elimination Method) Student Notes Look at each pair of terms below.

Term #1 Term #2 Answer Example 5x 10x Multiply Term #1 by: 2 Example 12y 4y Multiply Term #2 by: -3 6x 30x 2x 4x y y 2x 3x SECTION 2: STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: Solving Systems using the

2 SECTION 1: Warm-up Activity Lesson System of Equations (Elimination Method) Student Notes Look at each pair of terms below. Determine what you can multiply one (or both) terms by to make them cancel each other out. Term #1 Term #2 Answer Example 5x 10x Multiply Term #1 by: 2 Example 12y 4y Multiply Term #2 by: -3 6x 30x 2x 4x y y 2x 3x SECTION 2: STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: Solving Systems using the Elimination Method Line up the two equations in Standard Form. Eliminate one of the variables. To do this, look for coefficients that have the same variable but with opposite signs. If this does not exist, multiply one or both of the equations by a number that will create this situation. Combine to make one equation. Then solve that equation. Use the resulting answer to find the other variable by plugging it into either one of the original equations. Example 1: Example 2: You Try 1) 3x + 2y = 8 3x + 4y = 16 2 P a g e

3 Guided Practice 1) 9x + y = 13 3x + 2y = 4 You Try 2) 6x + 2y = 10 3) 7x 6y = 4 4) 6x 4y = 34 x + 12y = 34 3x + 2y = 11 2x 3y = 10 SECTION 3: Real-World Systems of Equations 1) The Sunny Meadows Safe Haven for Pets charge $200 to adopt a dog and $100 to adopt a cat. On April 30, National Adopt a Pet Day, 20 pets were adopted and $3,200 was collected. PART A: Write a system of equations to represent this situation. PART B: Solve the system to determine how many of each were adopted. Dogs adopted: Cats adopted: 2) The admission at a fair is $2 for children and $4 for adults. On a certain day 500 people enter the fair and $1,300 is collected. PART A: Write a system of equations to represent this situation. PART B: Solve the system. How many child admissions were there? How many adult admissions were there? 3 P a g e

4 Name Date Period: Classwork Lesson System of Equations Using the Elimination Method Solve each system of equations by elimination. Write your answer as a coordinate pair (x, y). 1. x + y = x + 4y = x + y = 4 x y = 2-3x 2y = -3-2x + y = x + 2y = x 2y = x 6y = 8-2x + 2y = 2 3x + 6y = 9 2x + 2y = x y = x 3y = x + 3y = -9-2x + y = -3-2x + 3y = -2 2x 5y = Tatiana and Jill each improved their yards by planting rose bushes and geraniums. They bought supplies at the same store. Tatiana spent $210 on 9 rose bushes and 12 geraniums. Jill spent $40 on 3 rose bushes and 1 geranium. Find the cost on one rose bush and the cost of one geranium. 4 P a g e

5 Name Date Period: Extra Practice Lesson System of Equations P a g e

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7 SECTION 1: Warm-up Activity Lesson System of Equations (Elimination Method) Student Notes Look at each pair of terms below. Determine what you can multiply one (or both) terms by to make them cancel each other out. Term #1 Term #2 Answer Example 5x 10x Multiply Term #1 by: 2 Example 12y 4y Multiply Term #2 by: -3 6x 30x Multiply Term#1 by: 5 2x 4x Multiply Term#2 by: -2 y y Multiply either by: -1 2x 3x Multiply Term#1 by: 3 Multiply Term#2 by: 2 SECTION 2: STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: Solving Systems using the Elimination Method Line up the two equations in Standard Form. Eliminate one of the variables. To do this, look for coefficients that have the same variable but with opposite signs. If this does not exist, multiply one or both of the equations by a number that will create this situation. Combine to make one equation. Then solve that equation. Use the resulting answer to find the other variable by plugging it into either one of the original equations. Example 1: Example 2: You Try 1) 3x + 2y = 8 3x + 4y = 16 (0,4) 7 P a g e

8 Guided Practice 1) 9x + y = 13 (2,-5) 3x + 2y = 4 You Try 2) 6x + 2y = 10 3) 7x 6y = 4 4) 6x 4y = 34 x + 12y = 34 3x + 2y = 11 2x 3y = 10 (-3, 4) (-2, -3) (1, 4) SECTION 3: Real-World Systems of Equations 1) The Sunny Meadows Safe Haven for Pets charge $200 to adopt a dog and $100 to adopt a cat. On April 30, National Adopt a Pet Day, 20 pets were adopted and $3,200 was collected. PART A: Write a system of equations to represent this situation. c + d = c + 200d = 3200 PART B: Solve the system to determine how many of each were adopted. Dogs adopted: 12 Cats adopted: 8 2) The admission at a fair is $2 for children and $4 for adults. On a certain day 500 people enter the fair and $1,300 is collected. PART A: PART B: Write a system of equations to represent this situation. c + a = 500 2c + 4a = 1300 Solve the system. How many child admissions were there? 350 How many adult admissions were there? P a g e

9 Name Answer Key Date Period: Classwork Lesson System of Equations Using the Elimination Method Solve each system of equations by elimination. Write your answer as a coordinate pair (x, y). 1. x + y = x + 4y = x + y = 4 x y = 2-3x 2y = -3-2x + y = 2 Answer: (7, 5) Answer: (-1, 3) Answer (2, 6) 4. 6x + 2y = x 2y = x 6y = 8-2x + 2y = 2 3x + 6y = 9 2x + 2y = 18 Answer: (1, 2) Answer: (2, ½) Answer: (5, 4) 7. 2x y = x 3y = x + 3y = -9-2x + y = -3-2x + 3y = -2 2x 5y = -16 Answer: infinitely many Answer: no solution Answer: (-3, 2) 10. Tatiana and Jill each improved their yards by planting rose bushes and geraniums. They bought supplies at the same store. Tatiana spent $210 on 9 rose bushes and 12 geraniums. Jill spent $40 on 3 rose bushes and 1 geranium. Find the cost on one rose bush and the cost of one geranium. 9r + 12g = $210 3r + g = $40 Answer: r = $10 g = $10 9 P a g e

10 Name Answer Key Date Period: Extra Practice Lesson System of Equations one Infinitely many none one Solution: (1, 3) 7. Solution: (4, -1) 10 P a g e

6-3 Solving Systems by Elimination

6-3 Solving Systems by Elimination Warm Up Simplify each expression. 1. 2y 4x 2(4y 2x) 2. 5(x y) + 2x + 5y Write the least common multiple. 3. 3 and 6 4. 4 and 10 5. 6 and 8 Objectives Solve systems of linear equations in two variables