Linear Functions and Applications

Lesson 8

Math

Unit 1

11th Grade

Lesson 8 of 13

Objective


Solve a system of three equations in three variables.

Common Core Standards


Core Standards

  • A.REI.C.6 — Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Foundational Standards

  • 8.EE.C.8

Criteria for Success


  1. Describe that a system of three variables is a system of three lines in three dimensions. 
  2. Identify graphing as an inefficient method to solve a system of three equations in three variables because of the necessity for three dimensions. 
  3. Identify an efficient method(s) to solving a system of three variables, focusing on elimination and substitution. 
  4. Describe conditions under which a system of three equations does not have a solution.
  5. Identify the solution to a system in three variables in the context of the problem. 

Tips for Teachers


  • Students will not need to know how to graph in three variables, just how to solve a system in three variables. 
  • Anchor Problem #2 is an old SAT problem, but the format of solving a system and then performing an operation with the solution coordinates continues through to the new SAT. 
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Anchor Problems

25-30 minutes


Problem 1

Determine the values for $${x, y}$$, and $$z$$ in the following system: 

$$2x + 3y - z =5$$

$$4x - y -z = -1$$

$$x + 4y + z = 12$$

Guiding Questions

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References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 30Example 1

Algebra II > Module 1 > Topic C > Lesson 30 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..

Problem 2

In a bicycle shop, there are different numbers of bicycles, tricycles, and tandem bikes. There are a total of 144 front-steering handlebars, 378 pedals, and 320 wheels. 

Below is a chart of how many front-steering handlebars, pedals, and wheels each vehicle contains. 

How many bicycles, tricycles, and tandem bikes are in the shop? 

Guiding Questions

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References

We Teach NYC The Cycle Shop

Target Task

5-10 minutes


For the following system, determine the values of $${p, q,}$$ and $$r$$ that satisfy all three equations: 

$$2p + q - r =8$$

$$q + r = 4$$

$${p- q =2}$$

References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 30Exit Ticket

Algebra II > Module 1 > Topic C > Lesson 30 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.

Next

Identify the solution to a system of an absolute value equation and a linear function algebraically and graphically.

Lesson 9
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Lesson Map

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

Topic A: Features of Linear Functions

Topic B: Systems of Functions and Constraints

Topic C: Piecewise Functions

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