Systems of Linear Equations

Lesson 1

Math

Unit 6

8th Grade

Lesson 1 of 11

Objective


Define a system of linear equations and its solution.

Common Core Standards


Core Standards

  • 8.EE.C.8.A — 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.

Foundational Standards

  • 6.EE.B.5
  • 8.F.B.4

Criteria for Success


  1. Define a system of linear equations as a set of two or more equations that involve the same variables.
  2. Understand that the solution to a system of linear equations is the point(s) that satisfy all of the equations in the system simultaneously, or graphically, the point(s) where the lines all intersect.
  3. Identify the solution to a system of equations represented in a graph. 
  4. Prove algebraically that a solution to a system satisfies all equations in the system. 

Tips for Teachers


  • In introducing the concept of a system of linear equations, it may be valuable to draw upon examples of systems in the real world (such as the solar system, the respiratory system, a game system, or our system of government). This can highlight that a system has at least two working parts and that the parts work together or are related in some way. 
  • This lesson draws on concepts from Unit 5, particularly constructing equations from points in a graph. Students may need to review these concepts alongside the lesson.
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Anchor Problems


Problem 1

Consider the graph below, showing two lines: L1 and L2.

a.   What is the equation for each line?

b.   Find a point, other than the ones given in the graph, that is a solution to L1 but not L2.

c.   Is the point (4, 21) a solution to L1? Is it a solution to L2? Justify your response using your equations from Part (a).

Guiding Questions

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References

Illustrative Mathematics Two Lines

Two Lines, accessed on March 10, 2017, 11:13 a.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 2

Estimate the solution to each system graphed below. 

a.   

b.   

Guiding Questions

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Problem 3

A system of linear equations and the corresponding graph are shown below. 

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

$${y={-{2\over3}}x+4}$$

Identify the solution to the system and then prove the solution algebraically.

Guiding Questions

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Problem Set

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Target Task


A system of linear equations is represented in the graph below. 

a.   Write the two equations that represent this system.

b.   What is the solution to the system? Prove this algebraically. 

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 examples where students identify the solution in graphs. (Only include unique solutions for now. Include solutions that do not have integer coordinate points.)
  • Include examples where students must prove a solution to a system algebraically.
  • Include examples where students are given two equations and select the point that is the solution to the system (no graphing involved).
  • Smarter Balanced Assessment Consortium: Item and Task Specifications MAT.08.TE.1.000EE.D.147
  • Illustrative Mathematics The Intersection of Two LinesThis problem is great to solidify the concepts from the lesson and have students explain systems in their own words.
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Lesson 2

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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