Systems of Linear Equations

Lesson 5

Math

Unit 6

8th Grade

Lesson 5 of 11

Objective


Solve systems of linear equations using substitution when one equation is already solved 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. Understand substitution as an algebraic approach to solving a system of equations.
  2. Understand that the method of substitution replaces one of the variables in the system with an expression in order to solve for the remaining variable.
  3. Look for and make use of the structure of equations in a system to identify which expression to substitute into which equation (MP.7).
  4. Use substitution to solve systems of equations.

Tips for Teachers


  • This is the first of three lessons on substitution. In Lesson 5, students focus on the concepts behind substitution and why it works. They look at problems where at least one equation has already been solved for $$x$$ or $$y$$, and problems that have a unique solution. In Lesson 6, students will solve an equation first before substituting, and they will look at examples with no or infinite solutions. Finally in Lesson 7, students will apply this strategy of solving systems to real-world applications. 
  • Common misconceptions include choosing expressions that are not equal to a single $$x$$ or a single $$y$$; substituting an expression into the same equation that it came from (not using both equations in the system); or finding only one value and forgetting to find the value of the other variable in the coordinate point.
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Anchor Problems

25-30 minutes


Problem 1

One equation is shown below:

$${3x+y=11}$$

a.   If you are given that $${y=-1}$$, can you find the value of $$x$$?

b.   If you are given that $$y=x-1$$, can you find the value of $$x$$?

Guiding Questions

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Student Response

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Problem 2

Solve the system below using substitution. Write your final answer as a coordinate point.

$${2x-y=16 }$$

$${y=14x+20}$$

Guiding Questions

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Student Response

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Problem 3

In each system below, circle the expression that you will substitute and draw an arrow to the appropriate variable and equation you will substitute it in for. There may be more than one approach for a system. You do not need to solve the systems.

a.   
 $$x=2y+4$$

$$4y-8=x$$

b.   
 $$y=-x$$

$$5x+5y=10$$

c.   
$$-3x+9=4y$$

$$x=y-3$$

d.    
$$\frac{1}{2}x=2y+4$$

$$y=4x-1$$

e.    
$$y=3x+2$$

$$y=-3x+1$$

f.    
$$x=y$$

$$\frac{4}{5}x-6y=15$$

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


Solve the system using substitution. Write your answer as a coordinate point. 

$${x=2y+4 }$$
$${4y-8=x}$$

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; only include problems where one of the equations is already solved for
  • Examples where students solve using substitution and verify by graphing

Next

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

Lesson 6
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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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