Curriculum  /  Math  /  9th Grade  /  Unit 4: Linear Equations, Inequalities and Systems  /  Lesson 9

Linear Equations, Inequalities and Systems

Lesson 9

Math

Unit 4

9th Grade

Lesson 9 of 14

Objective

Solve a system of linear equations graphically.

Common Core Standards

Core Standards

  • A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
  • A.REI.D.11 — Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.EE.C.8

Criteria for Success

  1. Describe that the solution to a system of equations is the intersection point of the lines in the graph or a point that satisfies all equations. 
  2. Use the relationship between variables to write multiple functions that form a system of equations. 
  3. Describe the solution to a system of equations in the context of the problem.

Tips for Teachers

This lesson builds on work that students have done in grade 8 with systems of linear equations. Solving by graphing is taught first in this series on systems to provide a basis for systems of linear inequalities in the next lesson. 

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

Draw a system of linear equations with a solution of $${(-1,3)}$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

You work for a video streaming company that has two monthly plans to choose from: 

  • Plan 1: A flat rate of $7 per month plus $2.50 per video viewed
  • Plan 2: $4 per video viewed

Write and graph an equation for each plan on a coordinate plane. 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Video Streaming

Video Streaming, accessed on Oct. 19, 2017, 3:27 p.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 3

What is the solution to the systems shown below? 

$${\left\{\begin{matrix}y=3x+2 \\ 2y=6x-8 \end{matrix}\right.}$$

Change the system so that it has ALL the same solutions.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

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

Construct a system of two linear equations where  $${(-2,3)}$$ is a solution to the first equation but not the second equation and where $${(5,-2)}$$ is a solution to the system. 

References

Illustrative Mathematics Find a System

Find a System, accessed on Oct. 19, 2017, 3:39 p.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.

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 the system of equations results in no solutions and others where the system of equations results in all solutions. Do this in context. 

Next

Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.

Lesson 10
icon/arrow/right/large

Lesson Map

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

Topic A: Properties and Solutions of Two-Variable Linear Equations and Inverse Functions

Topic B: Properties and Solutions of Two-Variable Linear Inequalities

Topic C: Systems of Equations and Inequalities

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free