ALEX | Alabama Learning Exchange

Systems of Two Linear Equations

Classroom Resource Information

Title:

Systems of Two Linear Equations

URL:

https://teacher.desmos.com/activitybuilder/custom/5807d7306ef115e7053a142a

Content Source:

Other
Desmos

Type:

Learning Activity

Overview:

Students will use a Desmos activity to solve systems of linear equations. In this activity, students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution." The activity closes by asking students to apply what they have learned to similar situations. This Desmos activity offers sample student responses and a teacher guide.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability

10. Select an appropriate method to solve a system of two linear equations in two variables.

a. Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

b. Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.

Unpacked Content

Evidence Of Student Attainment:

Students:

Choose an appropriate method for solving a system of two linear equations (e.g., substitution, addition, tables, graphing).
Solve and justify solutions.
Contrast solutions to a system of two linear equations to determine which method is more efficient.
Understand that tables and graphs of systems of equations my produce estimates rather than exact solutions.
Provide reasonable approximations when appropriate in a graph or table.

Teacher Vocabulary:

Solution of a system of linear equations
Substitution method
Elimination method
Graphically solve
System of linear equations
Solving systems by addition
Tabular methods

Knowledge:

Students know:

Appropriate use of properties of addition, multiplication and equality.
Techniques for producing and interpreting graphs of linear equations.
Techniques for producing and interpreting tables of linear equations.
The conditions under which a system of linear equations has 0, 1, or infinitely many solutions.

Skills:

Students are able to:

Accurately perform the operations of multiplication and addition, and techniques for manipulating equations.
Graph linear equations precisely.
Create tables and locate solutions from the tables for systems of linear equations.
Use estimation to find approximate solutions on a graph.
Contrast solution methods and determine efficiency of a method for a given problem situation.

Understanding:

Students understand that:

The solution of a linear system is the set of all ordered pairs that satisfy both equations.
Solving a system by graphing or with tables can sometimes lead to approximate solutions.
A system of linear equations will have 0, 1, or infinitely many solutions.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
ALGI.10.1: Solve a system of equations using three methods (Substitution, Elimination, and Graphing.
ALGI.10.2: Distinguish the similarities and differences between the three methods of solving systems of equations.

Prior Knowledge Skills:

Solve a system of equation by graphing.
Solve a system of equation by elimination.
Solve a system of equation by substitution.
Understand the meaning of the solution to a system of equations.
Graph a linear equation.

Alabama Alternate Achievement Standards

AAS Standard:
M.A.AAS.11.9 Identify equivalent expressions given a linear expression using arithmetic operations.

Tags:

linear equations, systems, systems of equations

License Type:

Custom Permission Type
See Terms: https://www.desmos.com/terms
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses

Accessibility

Text Resources: Content is organized under headings and subheadings

Comments

Desmos's mission is to help every student learn math and love learning math. Teachers can explore and enjoy Desmos collections of free digital math activities that include:

Meaningful feedback by showing students what their answers mean, then give them the opportunity to improve their thinking and revise their work.
Collaboration by using devices to connect students, not to isolate them. Students see their classmates' thinking. They ask each other questions and create challenges for each other.
Invite students to solve challenging problems using the tools they already have.

If the teacher does not have an account, he/she will need to create a FREE account. (More information on how Desmos works can be found at Getting Started.)

Once the teacher has selected an activity to run, he/she will need to click on the "Create Class Code" button. This will generate a unique class code and a link to view the dashboard. (More information can be found at Creating a Class Code.) Every new activity will need a new class code in order to start a session. Students cannot start the activity until they have the class code so sessions can be started days, hours, or mere minutes before the teacher plans to run the activity. When the teacher is ready to have students start, have the students go to student.desmos.com and enter the class code. Although it is not required, Desmos strongly encourages students to sign in with their Desmos Student Account. Signing in allows students to resume and view their past activity work.

This resource provided by:

Author:

YVETTE AKRIDGE

ALEX Classroom Resource

Systems of Two Linear Equations