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System of Equations by Substitution Guided Notes w/ Doodles | Linear Equations
$4.25
Overview
Get the Lesson Materials
System of Equations by Substitution Guided Notes w/ Doodles | Linear Equations
$4.25
Learning Objectives
After this lesson, students will be able to:
- Solve a system of linear equations using the substitution method
- Identify cases of system of linear equations with one solution, no solution, infinite solutions
- Apply the concept of substitution to real-world problems involving linear equations
- Demonstrate understanding of the topic by completing practice worksheets and a real-life application exercise
Prerequisites
Before this lesson, students should be familiar with:
- Solving one-step equations
- Understanding of linear equations and their graphs
Materials
- Pencils
- Colored pencils or markers
- System of Equations by Substitution Guided Notes w/ Doodles | Linear Equations
Key Vocabulary
- System of Equations
- Substitution
- Linear Equations
- Simultaneous Equations
Procedure
Introduction
As a hook, ask students why understanding how to solve systems of linear equations by substitution is important in real-life situations. Refer to the last page of the guided notes as well as the FAQs below for ideas.
Use the first page of the guided notes to introduce the concept of solving a system of two linear equations using substitution. Walk through the process of substituting one equation into the other to find the value of the variable. Identify cases where the system of linear equations by substitution will have one solution, no solution, or infinite solutions.
Repeat the instruction to teacher for each guided notes page, ensuring to cover key points such as identifying which equation to substitute, solving for one variable, and then back-substituting to find the other variable. Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, consider pulling out students for reteaching while having more advanced students start working on the practice exercises.
Practice
Have students practice solving system of linear equations through substitution using the maze (pg. 3 of guided notes) and color by code activity (pg. 4 of guided notes) worksheet. Walk around to answer student questions.
Fast finishers can dive into the real life application activity (pg. 5 of guided notes). You can assign any of the practice activities as homework for the remainder of the class.
Real-Life Application
Use the last page of the guided notes (pg. 5) to bring the class back together, and introduce the concept of solving a system of equations by substitution in real-life scenarios. Discuss how this mathematical skill can be used to solve problems in various fields such as economics, engineering, and science.
You can ask students to think about situations where two unknown values need to be determined simultaneously, like when calculating the cost of different items at a store, designing a structure with specific dimensions, or analyzing chemical reactions in a laboratory setting. Refer to the FAQ for more ideas on how to teach real-life applications of solving systems of equations by substitution!
Extensions
Additional Self-Checking Digital Practice
If you’re looking for digital practice for adding and subtracting numbers in scientific notation, 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:
Additional Print Practice
A fun, no-prep way to practice adding and subtracting numbers in scientific notation is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels levels of practice, perfect for a review day or sub plan.
Here are some activities to try:
FAQs
The substitution method is a technique used to solve a system of linear equations by isolating one variable in one equation and substituting it into the other equation.
Key Points:
- Isolate one variable in one of the equations.
- Substitute the expression for that variable into the other equation.
- Solve the resulting equation to find the value of the variable.
- Substitute this value back into one of the original equations to find the value of the other variable.
You should use the substitution method to solve a system of equations when one of the equations can be easily solved for one variable.
Key Points:
- Look for an equation where a variable is already isolated.
- Check if one of the equations can be rearranged to isolate a variable.
- Substitution is particularly useful when one equation is already solved for x or y.
Solving a system of equations by substitution involves a series of steps to find the values of the variables in the system.
Key Points:
- Isolate one variable in one of the equations.
- Substitute the expression for that variable into the other equation.
- Solve the resulting equation to find the value of the variable.
- Substitute this value back into one of the original equations to find the value of the other variable.
- Check your solution by substituting the values back into both equations.
Solving systems of linear equations is important as it allows us to find the points of intersection between two lines, which are solutions to both equations simultaneously.
Key Points:
- Helps in understanding relationships between multiple variables.
- Useful in optimization problems where multiple constraints exist.
- Applications in real-world scenarios like economics, physics, and engineering.
You can verify the solution obtained through the substitution method by plugging the values back into both equations to ensure they satisfy both equations simultaneously.
Key Points:
- Substitute the values of the variables into both original equations.
- Check that the equations hold true for the given values.
- If both equations are satisfied, the solution is correct.
When using the substitution method, it's essential to watch out for common errors that can lead to incorrect solutions.
Key Points:
- Forgetting to substitute the expression back into both equations.
- Making calculation errors when isolating variables.
- Incorrectly rearranging equations during the substitution step.
To practice solving systems of equations by substitution, you can work on various problems and exercises that involve substituting one equation into the other.
Key Points:
- Start with simple linear equations and gradually move to more complex systems.
- Use online resources, textbooks, and worksheets for additional practice.
- Check your answers and seek feedback to improve your skills.
Yes, solving systems of linear equations by substitution has practical applications in various fields, including economics, physics, and engineering.
Key Points:
- Used in cost analysis and budgeting to find optimal solutions.
- Helps in determining intersection points of various quantities.
- Used in designing structures and systems where multiple constraints are involved.