Systems of Linear Equations

Lesson 4

Math

Unit 6

8th Grade

Lesson 4 of 11

Objective


Solve real-world and mathematical problems by graphing systems of linear equations.

Common Core Standards


Core Standards

  • 8.EE.C.8.C — Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Foundational Standards

  • 8.F.B.4

Criteria for Success


  1. Write a system of two linear equations to represent a real-world situation.
  2. Solve a system of equations and interpret the solution in context of the situation. 
  3. Given two pairs of coordinate points that describe two lines, determine if the lines intersect.

Tips for Teachers


  • In terms of pacing, this lesson may extend over an additional day depending on your individual classroom. 
  • Encourage students to define their variables in each situation to ensure they are able to contextualize and de-contextualize as they work with real-world applications (MP.2).
Fishtank Plus

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

Anchor Problems

25-30 minutes


Problem 1

You and a friend are reading the same book over the summer. You have already read 35 pages of the book, and you set a goal to read 15 pages each day. Your friend has only read 15 pages so far but sets a goal to read 20 pages each day. 

a.   Write a system of linear equations to represent the situation and graph both lines on the coordinate plane below.

b.   After how many days will you both be on the same page?

c.   Who will have read more pages after 10 days? Explain how you got your answer.

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

One line passes through points (0, 2) and (4, 6). Another line passes through points (-3, 2) and (1, 6). Will the two lines intersect at a single point? If so, where? Use the coordinate plane if needed.

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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


Two companies offer a subscription service for listening to and downloading music by the month. The company Musik charges $5 a month for unlimited listening plus a $0.50 fee for every album that you download. The company Waves charges $8 a month for unlimited listening plus a $0.25 fee for every album that you download.

a.   Write and graph a system of linear equations to determine which company offers the better monthly deal based on the number of albums you download a month. Label your graph. 

b.   How many albums would you need to download for the costs to be the same?

c.   How many albums could you download per month for Musik to be the better deal?

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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 are given situations that can be represented with equations and graphed easily to determine the solution; examples with rates are good problems to include, such as speed, wages, costs, etc.
  • Include a combination of problems that include context and those that do not. 
  • Examples where students are given two pairs of coordinate points and must determine if the two lines intersect, and if so, where 

Next

Solve systems of linear equations using substitution when one equation is already solved for a variable.

Lesson 5
icon/arrow/right/large

Lesson Map

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

Topic A: Analyze & Solve Systems of Equations Graphically

Topic B: Analyze & Solve Systems of Equations Algebraically

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