Curriculum / Math / 8th Grade / Unit 6: Systems of Linear Equations / Lesson 3
Math
Unit 6
8th Grade
Lesson 3 of 11
Jump To
Classify systems of linear equations as having a unique solution, no solutions, or infinite solutions.
The core standards covered in this lesson
8.EE.C.8.A — Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In this lesson, students inspect equations of systems to determine how many solutions they have. They do not solve systems algebraically yet, as this will come later in the unit.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
You and a friend are going for a run along a path. You both run at the same exact speed, but your friend starts 100 yards ahead of the starting point which is where you start.
The graph below is a sketch of your and your friend’s distance traveled from the starting point over time. When will you and your friend be the same distance from the starting point? Explain your answer using the graph.
Graph the system of equations below.
$${y={1\over3}(x-6)}$$
$${6y=2x-12}$$
Anika was not sure how to interpret the graph of the system. She thought that since there was only one line visible in the graph then there were no solutions to the system of equations. Do you agree with Anika's reasoning? Explain why or why not.
Consider the equation $$y = \frac{2}{5} x + 1$$. Write a second linear equation to create a system of equations that has:
a. Exactly one solution
b. No solutions
c. Infinite solutions
How Many Solutions?, accessed on March 10, 2017, 12:03 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.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Determine if each system below has one, no, or infinite number of solutions. Explain your answer.
a. $${y=3x-2}$$
$${y=3x-3}$$
b. $${x+2y=-4}$$
$${5x+10y=-20}$$
c.
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.
Lesson 2
Lesson 4
Topic A: Analyze & Solve Systems of Equations Graphically
Define a system of linear equations and its solution.
8.EE.C.8.A
Solve systems of linear equations by graphing.
8.EE.C.8.A 8.EE.C.8.B
Solve real-world and mathematical problems by graphing systems of linear equations.
8.EE.C.8.C
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Analyze & Solve Systems of Equations Algebraically
Solve systems of linear equations using substitution when one equation is already solved for a variable.
8.EE.C.8.B
Solve systems of linear equations using substitution by first solving an equation for a variable.
Solve real-world and mathematical problems using linear systems and substitution.
Solve systems of linear equations using elimination (linear combinations) when there is already a zero pair.
Solve systems of linear equations using elimination (linear combinations) by first creating a zero pair.
Solve real-world and mathematical problems using systems and any method of solution.
8.EE.C.8.B 8.EE.C.8.C
Model and solve real-world problems using systems of equations.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free