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1.16 MB | 18 files, 1-2 pages each pages
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This file includes 18 resource files for an overview of systems of equations and inequalities:
- Solving by Graphing (including nonlinear systems*)
- Systems of Inequalities
- Solving by Substitution
- Solving by Elimination with and without Multiplication
- Application Problems
Note: This unit does NOT include anything about matrices.
* square root, absolute value, cubic, quadratic, exponential--see my Transformations mini-unit for more information about how I approach these problems
You will download a .zip file from which 18 .doc files can be extracted.
Each file includes a key for the notes and practice problems. The files include guided notes and homework. See descriptions below:
0 - Systems Intro Problem: A quick problem with a variety of entry points
1a - Is It a Solution: Practice checking to see if a given ordered pair is a solution of a system.
1b - Systems Intro: Introduction to the idea of systems, including classifying them as independent, etc.
2 - Solving by Graphing Notes: Guided notes for solving linear systems by graphing.
3 - Nonlinear Systems: Guided notes and practice for solving nonlinear systems by graphing, using parent graphs and transformations.
4 - Tough Looking Equations: Apply "nonlinear systems" ideas (above) to graphically solving equations where that equates two non-linear expressions.
5 - Systems of Inequalities: Guided notes and practice for solving systems of linear inequalities.
6a - Substitution - Notes: Guided notes for solving linear systems by substitution.
6b - Substitution - Practice: Individual practice for using the substitution method.
7 - Elimination No Multiplication: Guided notes and practice for solving linear systems by elimination (no multiplication required).
8a - Elimination with Multiplication - Notes: Guided notes for solving linear systems by elimination (multiplication necessary).
8b - Elimination with Multiplication - Practice: Individual practice for using the elimination method (multiplication necessary).
9 - Systems Summary: A one-page (front-to-back) summary of the methods for solving linear systems, with examples, and "when it's easy" notes.
10a - Systems Applications Notes: Guided notes to creating and solving a system of linear equations based on a problem context.
10b - Systems Word Problems Set Up: Practice setting up (not solving) systems of linear equations based on a problem context.
10c - Systems Word Problems Solve: Practice setting up and solving systems of linear equations based on a problem context.
11a - Systems of Inequalities Word Problems - Notes: Guided notes to creating and solving a system of linear inequalities based on a problem context.
11b - Systems of Inequalities Word Problems - HW: Practice setting up and graphing systems of linear inequalities based on a problem context.
Common Core Standards:
8.EE.8 Analyze and solve pairs of simultaneous linear equations
8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables.
A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables graphically
A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.
A-REI.12 Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.