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System of Equations by Graphing Guided Notes w/ Doodles | Simultaneous Equations
$4.25
Overview
- Standards: CCSS 8.EE.C.8, CCSS 8.EE.C.8.a, CCSS 8.EE.C.8.b
- Unit: 8th Grade → Unit 3: Linear Equations & Systems of Equations
- Grade: 8th Grade
Get the Lesson Materials
System of Equations by Graphing Guided Notes w/ Doodles | Simultaneous Equations
$4.25
Learning Objectives
After this lesson, students will be able to:
- Identify characteristics of systems of equations can have one solution, no solutions, or infinite solutions
- Graph pairs of simultaneous linear equations (system of linear equations) to solve for the solution
- Identify the solution of a system of equations by determining the point of intersection on the graph (in the case of one solution)
- Interpret the real-life applications of solving systems of equations through graphing
- Identify real life applications of system of equations
Prerequisites
Before this lesson, students should be familiar with:
- Knowledge of solving one-step and two-step equations
- Ability to plot points on a coordinate plane
- Familiarity with graphing linear equations in slope-intercept form
Materials
- Pencils
- Colored pencils or markers
- System of Equations by Graphing Guided Notes w/ Doodles | Simultaneous Equations
Key Vocabulary
- System of Equations
- Linear Equations
- Graphing
- Simultaneous Equations
Procedure
Introduction
As a hook, ask students why understanding how to solve a system of linear equations by graphing 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 by graphing. Identify cases of graphs of system of linear equations with one solution (intersection), no solution (parallel lines) or infinite solutions (overlapping lines). Then, walk through the steps involved in graphing each equation on the coordinate plane and finding the point of intersection (in the case of one solution).
Repeat the instruction for the second page of the guided notes. Students are provided with practice examples of pairs of linear equations through graphing. Ensure students understand the relationship between the graph and the solution.
Based on student responses, reteach concepts that students need extra help with regarding graphing linear equations and finding solutions. If your class has a wide range of proficiency levels, consider pulling out students for reteaching while more advanced students start working on the practice exercises.
Practice
Have students practice solving systems of linear equations by graphing using the practice worksheet included in the resource (pg. 2) as well as the maze activity (pg. 3), and color by number worksheets (pg. 4). Monitor the class as they work through the problems and offer assistance as needed.
Fast finishers can proceed to the maze activity provided in the resource for additional practice. You may assign it as homework for those who complete the practice worksheet early.
Real-Life Application
Using the last page of the guided notes (pg. 5), bring the class back together, and introduce the concept of using system of equations by graphing to analyze scenarios in the real world where multiple linear relationships intersect.
This could involve situations like determining the break-even point for a business, analyzing the intersection of supply and demand curves in economics, or understanding the point of equilibrium in physics problems.
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
A system of equations by graphing is a method used to solve a set of linear equations by plotting them on the coordinate plane and finding the point of intersection.
- Students graph each equation on the coordinate plane.
- The solution is where the graphs intersect.
To graph a system of equations:
- Plot the y-intercept of each equation, if it's not in slope-intercept form.
- Use the slope to plot additional points on each line.
- Draw a line through the points to represent each equation.
- The solution is where the lines intersect on the graph.
Solving systems of equations by graphing helps in understanding:
- How two different linear equations can relate to each other.
- The concept of a solution being the point of intersection.
- Graphical representation of mathematical concepts.
Simultaneous equations can be represented graphically by:
- Drawing each equation as a line on the coordinate plane.
- Identifying the point where the lines intersect.
- This point represents the solution to the system of equations.
Graphing is a useful method for solving systems of equations because:
- It provides a visual representation of the equations.
- It helps students understand the concept of solutions as points of intersection.
- It can be a helpful tool for students who are visual learners.
Real-life applications of solving systems of equations by graphing include:
- Determining the optimal combination of resources in business.
- Calculating the break-even point in economics.
- Analyzing intersections of paths in navigation systems.