Systems of Linear Equations

Lesson 6

Math

Unit 6

8th Grade

Lesson 6 of 11

Objective


Solve systems of linear equations using substitution by first solving an equation for a variable.

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. Rewrite an equation in a system so it is solved for either $$x$$ or $$y$$ in order to substitute it into the other equation. 
  2. Look for and make use of the structure of equations in a system to identify which expression to substitute into which equation and to identify when a system has no or infinite solutions (MP.7).
  3. Use substitution to solve systems of equations.

Tips for Teachers


This is the second of three lessons on substitution. In Lesson 6, students solve an equation for a variable first before substituting, and look at examples with no or infinite solutions. In Lesson 7, students will apply this strategy of solving systems to real-world applications.

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Anchor Problems

25-30 minutes


Problem 1

Solve the system of linear equations using substitution. Describe how you can solve any system using substitution.

$${x+2y=8}$$
$${-3x+2y=16}$$

Guiding Questions

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Student Response

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Problem 2

Solve the two systems below using substitution. Compare and contrast the two solutions. What do they each mean?

System A System B

 $${y=2(-x+3)}$$

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

 $${5x+20y=15}$$

$${x+4y=3}$$

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


Determine by inspection if each system below has a unique solution, no solution, or infinite solutions. If the system has a unique solution, use substitution to find the coordinate point where the two lines intersect.

a.   

$${y=-3x+5}$$

$${2y=-6x+10}$$

b.   

$${x+y=8}$$

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

c.   

$${x+y=3}$$

$${2x+2y=3}$$

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.

  • Examples where students solve systems using substitution; include problems where an equation must be solved for a variable first; include problems that have no solution or infinite solutions; include problems where the solution includes fractions or decimals; spiral in review of graphing to verify solutions

Next

Solve real-world and mathematical problems using linear systems and substitution.

Lesson 7
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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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