Linear Equations with One Solution, Infinite Solutions, and No Solution

Introduction

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As a hook, ask students why linear equations are important in real life situations. For example, ask them how they might use linear equations to solve problems related to budgeting or predicting future costs. Refer to the last page of the guided notes, which includes a real-life math application, for ideas.

Use the first page of the guided notes to introduce the concept of linear equations with one solution. Walk through the guided notes, explaining key points such as how to identify linear equations with one solution, no solution, or infinite solutions. This includes modeling with the scale and completing an example for each scenario. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Practice

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Have students practice solving linear equations with one solution, infinite solutions, and no solutions using the practice worksheet (pg. 2) included in the resource. They can complete the maze (pg. 3) and color by code (pg. 4) to reinforce the concepts learned in the guided notes.

Walk around the classroom to answer any questions students may have and provide support as needed.

For fast finishers, they can continue practicing with the real-life application activity included in the resource. This activity allows students to read and write about real-life uses of solving linear equations with different solutions.

Real-Life Application

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Use the last page of the guided notes to bring the class back together, and introduce the concept of real-world applications of linear equations with one solution, infinite solutions, or no solution. Explain that linear equations can be used to model real-life situations and solve problems.

Additional examples of real-life applications include:

• Setting up a lemonade stand: Use linear equations to determine the cost of supplies and the number of cups of lemonade sold in order to break even.
• Planning a road trip: Use linear equations to calculate the distance, time, and speed needed to reach a destination.
• Analyzing cell phone plans: Use linear equations to compare different plans based on the number of minutes used and the cost per minute.

Refer to the FAQ for more ideas on how to teach real-life applications of linear equations.

Additional Self-Checking Digital Practice

If you’re looking for digital practice for linear equations with one solution, infinite solutions, or no solution, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here are some activities to explore:

• [Free] Equations with One, No, or Infinite Solutions Pixel Art Activity