Types of Solutions: Systems of Equations
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Subject Area: Mathematics (B.E.S.T.) | Grade Level: 8
Lesson Length: 45 minutes
Keywords/Tags: systems of equations; types of solutions
Lesson Description: Students should be able to analyze and explain the solutions to systems of equations presented numerically, algebraically, and graphically. When examining a graph, students should explain the significance of the point of intersection in a given context.

  • MA.8.AR.4.2 Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution or infinitely many solutions.
  • MA.8.AR.4.3 Given a mathematical or real-world context, solve systems of two linear equations by graphing.
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Video : One Solution, No Solution, or Infinitely Many Solutions - Consistent & Inconsistent Systems
Instructions: Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.
Description: This algebra video tutorial explains how to determine if a system of equations contain one solution, no solution, or infinitely many solutions. It also explains how to determine if the solution is consistent or inconsistent as well as dependent or independent.
Quiz : Types of Solutions to Systems of Equations
Instructions: Please complete this quiz by choosing the correct answer for each question. You can take this quiz as many times needed.
Question #1

Determine the number of solutions of the linear system:

14x – 5y = 123
14x – 5y = 73

Question #2
Describe the difference between a solution that is consistent and an inconsistent one.
Question #3

If a system of linear equations has one solution, what does this mean about the two lines? 

Question #4

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

Question #5

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

Description: Read each question carefully. Decide if there is one solution, no solution, or infinitely many solutions.
Assignment : Quizziz: Solutions to Systems

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