Systems of Linear Equations

Lesson 8

Math

Unit 6

8th Grade

Lesson 8 of 11

Objective


Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.

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.

Foundational Standards

  • 8.EE.C.7

Criteria for Success


  1. Understand that adding equivalent expressions will maintain the equivalence; equations can be added together. 
  2. Understand elimination as an algebraic approach to solving a system of equations.
  3. Define and identify zero pairs in systems of equations. 
  4. Solve systems of equations using elimination. 

Tips for Teachers


This is the first of two lessons on solving systems using elimination or linear combinations. In Lesson 8, students focus on the concepts behind elimination and why it works. Students look at problems that already contain a zero pair and do not require multiplication. In Lesson 9, students will learn how to multiply one or both equations in order to use this method. 

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Anchor Problems

25-30 minutes


Problem 1

Investigate if you can add equations to each other and still maintain balance and equality. 

a.   Given:

$$2 + 5 = 7$$, and

$$1 + 9 = 10$$

Does $$(2 + 5) + (1 + 9) = 7 + 10$$?

Does $$(2+1) + (5+9) = 7 + 10$$?

b.   Given

$$-3 + 11 = 8$$, and

$$7 - 2 = 5$$

Does $$ (-3 + 11) + (7 - 2) = 8 + 5$$?

Does $$(-3 + 7) + (11 - 2) = 8 + 5$$?

c.   Based on your conclusion from parts (a) and (b), write a single equation that accounts for both equations below.

$$x + 3 = 8 $$

$$x - 4 = 1$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic D > Lesson 28Example 1

Grade 8 Mathematics > Module 4 > Topic D > Lesson 28 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

Solve the system of equations below by using the elimination method. Write your answer as a coordinate point. 

$${6x-5y=21}$$

$${2x+5y=-5}$$

Guiding Questions

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Student Response

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Problem 3

Solve the three systems using the elimination method. Compare and contrast each solution.

System A System B System C

$${{{4y+2x=12}}}$$

$${-4y-2x=12}$$

$${{{4y+2x=12}}}$$

$${-4y-2x=-12}$$

$${{{4y+2x=12}}}$$

$$-{{{4y+2x=12}}}$$

Guiding Questions

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Student Response

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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

Tamar writes two equations:

$$2y=4x+14$$

$$-2y=-4x-14$$

Tamar says that together, the two equations create a system with no solution because both equations have the same slope. 

Do you agree with Tamar? Explain your reasoning. 

Student Response

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Problem 2

Solve the system.

$${9x+2y=9}$$
$${6x-2y=-4}$$

Student Response

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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 problems where students solve systems using elimination to reinforce the procedure and process; ensure problems all have a zero pair and do not yet require multiplication; include problems that are no solution or infinite solution.

Next

Solve systems of linear equations using elimination (linear combinations) by first creating a zero pair.

Lesson 9
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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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