Systems of Linear Equations

Lesson 10

Math

Unit 6

8th Grade

Lesson 10 of 11

Objective


Solve real-world and mathematical problems using systems and any method of solution.

Common Core Standards


Core Standards

  • 8.EE.C.8.B — 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.8.C — 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.

Foundational Standards

  • 8.EE.C.7
  • 8.F.B.4

Criteria for Success


  1. Look for and make use of structure in equations to determine an efficient method to solve a system of equations (MP.7).
  2. Write a system of equations to represent a situation and interpret the solution in context. 
  3. Solve systems of equations using any strategy.

Tips for Teachers


Lessons 10 and 11 bring the concepts of the unit together. This is a good opportunity for students to focus on targeted concepts or skills where they still need practice or development. 

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Anchor Problems

25-30 minutes


Problem 1

Which method—graphing, substitution, or elimination—would you choose to solve each system below? Explain your answer.

System A System B System C

$${y={2\over3}x-6}$$

$${y=-{x\over4}+2}$$

$${1.5x-6.2y=18.3}$$

$${1.5x+6.2y=-4.8}$$

$${x=3(y+1)}$$

$${2x+4y=-7}$$

Guiding Questions

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Student Response

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Problem 2

The sum of two numbers is 361, and the difference between the two numbers is 173. What are the two numbers?

Write a system of equations to represent the information above. Solve it using any method. 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 29Example 1

Grade 8 Mathematics > Module 4 > Topic D > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage of each ingredient in the blend, but we know that the quinoa in the blend contains 16.2% protein and the corn in the blend contains 3.5% protein. Overall, each 57-gram serving of pasta contains 4 grams of protein. How much quinoa and how much corn is in one 57-gram serving of the pasta?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Quinoa Pasta 1

Quinoa Pasta 1, accessed on March 12, 2017, 6:53 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Problem 1

Small boxes contain Blu-ray disks and large boxes contain one gaming machine. Three boxes of gaming machines and a box of Blu-rays weigh 48 pounds. Three boxes of gaming machines and five boxes of Blu-rays weigh 72 pounds. How much does each box weigh?

Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 29Exit Ticket, Question #1

Grade 8 Mathematics > Module 4 > Topic D > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

A language arts test is worth 100 points. There is a total of 26 questions. There are spelling word questions that are worth 2 points each and vocabulary questions worth 5 points each. How many of each type of question are there? 

Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 29Exit Ticket, Question #2

Grade 8 Mathematics > Module 4 > Topic D > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include a variety of problems for students to solve, with and without context, that may be efficiently solved with the three different strategies.
  • Challenge: Two friends travel along a straight path towards one another. One friend starts at mile marker 0 and runs 6 miles per hour. The other friend starts at mile marker 12. If the two friends meet up at mile marker 8 after 1 hour and 20 minutes, how fast was the second friend traveling?

Next

Model and solve real-world problems using systems of equations.

Lesson 11
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Analyze & Solve Systems of Equations Graphically

Topic B: Analyze & Solve Systems of Equations Algebraically

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