Activity
Undetermined points and systems of linear equations 3: Solving a linear equation
In Part 3, students solve linear equations to uncover missing values and connect algebra to graphs—one equation at a time!
In this third post of the Undetermined Points and Systems of Linear Equations series, students shift their focus from identifying unknown coordinate points to solving linear equations algebraically. Building on earlier lessons that paired tactile graphing and Desmos exploration, this activity challenges students to use auditory graph feedback and digital tools to understand how a single equation can represent a line—and how solving that equation helps identify missing values. Whether working from an equation or interpreting a graph, students begin connecting algebraic reasoning with visual and spatial representations of linear relationships.
Activity 3: Use a system to solve a linear equation
By this point, students should have solved linear equations with one variable using inverse operations. Another way to solve a linear equation with one variable is by graphing and solving a system of equations based on the given linear equation. You may notice that this is not so dissimilar to what you have done in Activities 1 and 2 in this set. To solve an equation with one variable, write a system using both sides of the equation. Then use the Audio Trace feature in Desmos to solve the system.
Note: Some screen readers have trouble reading math equations in this website. For a fully accessible version of this post, download the accessible Word document, Solving a Linear Equation.
Objective
- Solve a linear equation using a system of equations in the Desmos graphing calculator.
Materials needed
- PC laptop or desktop with JAWS
- Internet browser
Lesson/activity sequence
Linear equation with the variable on one side
Problem: Use a system of equations to solve 5x + 6 = -4.
Step 1: Write a system of equations. Set each side of the equation equal to y.
y = 5x + 6
y = -4
Step 2: Enter these equations in the expression list and graph in the standard viewing window.
Image 1:
Step 3: Audio trace either one of the two equations. Use the points of interest keys (k and i) to determine the intersection of the two equations.
Image 2:
Step 4: Create a point at the intersection using an ordered pair in expression 3 and label the point.
Image 3:
The solution is x = -2. You can check this by substituting – 2 into the original equation.
5x + 6 = -4
5(-2) + 6 = -4
-10 + 6 = -4
-4 = -4
True.
Linear equation with the variable on both sides
Problem: Use a system of equations to solve 3x + 12 = -5x – 18.
Step 1: Write a system of equations. Set each side of the equation equal to y.
y = 3x + 12
y = -5x – 18
Step 2: Enter these equations in the expression list and graph in the standard viewing window.
Image 4:
Step 3: Audio trace either one of the two equations. Use the points of interest keys (k and i) to determine the intersection of the two equations.
Image 5:
Step 4: Create a point at the intersection using an ordered pair in expression 3 and label the point.
Image 6:
The solution is x = -3.75. You can check this by substituting -3.75 into the original equation.
3x + 12 = -5x – 18
3(-3.75) + 12 = -5(-3.75) – 18
-11.25 + 12 = 18.75 – 18
.75 = .75
True.
In this activity set, we have graphed systems of equations on the pegboard and on the Desmos graphing calculator. We have determined unknown points on a line using navigation in the Audio Trace feature of Desmos, as well as by using a system of equation. Finally, we solved a linear equation using a system of equations. In the next activity set, we will practice inequalities and systems of inequalities.
Resources
Activity set 1, Graphing Concepts series:
- Graphing concepts activity 1: Attributes and coordinates
- Graphing concepts activity 2: Plotting points
- Graphing concepts activity 3: Graphing a line
Activity set 2, Graph Board to Desmos series:
- Post 1: Setting up Jaws for Desmos
- Post 2: Plotting points and navigating Audio Trace
- Post 3: Representing functions in Desmos
- Input functions into the expression list
- Create tables from functions
- Navigate tables
- Editing expressions
- Sharing a graph
Activity set 3, Linear Functions and Problem Solving series (y-intercept and slope) series:
- Linear functions and problem solving 1: y-intercept and slope on a graph board
- Linear functions and problem solving 2: y-intercept and slope using Desmos
- Linear functions and problem solving 3: y-intercept and slope problem solving
Activity set 4, Undetermined points and systems of linear equations series:
- Undetermined points and systems of linear equations: What’s the Point activity 1
- Undetermined points and systems of linear equations 2: Finding the intersection
- Undetermined points and systems of linear equations 3: Solving a linear equation
Activity set 5: Inequalities and systems of inequalities series:
- Inequalities and systems of inequalities part 1: Simple inequalities
- Inequalities and systems of inequalities part 2: Linear inequalities
- Inequalities and systems of inequalities part 3: Systems of inequalities
Additional math resources by TEAM Initiative:
- TEAM Initiative web page
- Digital math: Introducing skill level checklists
- Digital math: Workflows from teacher to student and student to teacher
Pegboard post:
This algebra post was created as part of the TEAM Initiative to assist Teachers of Students with Visual Impairments (TSVIs) in teaching students digital math tools and to use tactile resources to support digital concepts. Written by John Rose. If you would like more information about the TEAM Initiative, contact Leslie Thatcher at [email protected].
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