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Module - Systems of Equations
Lesson 1 - Graphing Systems of Equations

Lessons

1-

Graphing Systems of Equations

2-

Solving Systems by Substitution

3-

Solving Systems by Elimination Using Addition and Subtraction

4-

Solving Systems by Elimination Using Multiplication

5-

Solving Systems of Inequalities by Graphing

6-

Module Review

 

 
SOL

A.4e -The student will solve multistep linear and quadratic equations in two variables, including solving systems of two linear equations in two variables algebraically and graphically.

Investigating Linear Systems in Slope-Intercept Form

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Investigating Linear Systems in Standard Form

[Remember: In Standard Form, slope = -(A/B) and y-intercept = C/B.

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Parallel Lines

Lines 1 and 2 can be manipulated by moving the corresponding sliders. Click and drag the sliders.

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Solve a system of linear equations in Standard Form:
Ax + By = C

Enter values of A, B and C in the spreadsheet for the two equations your are trying to solve. You will need to click the link below and open a new window to do this.
After you have solved your system, click on the checkbox to reveal the solution.

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Common Core Standards
8.EE.8a 8.EE.8b 8.EE.8c A-CED.3 A-REI.5 A-REI.6 A-REI.11
Warm-up
  1. Warm-up: Solving for y (doc)
Lessons
  1. Notes: Solving Systems by Graphing (ppt)
Videos
  1. Video: PH Solving a System of Equations by Graphing
  2. Video: PH Interpreting Solutions to Systems of Equations
  3. Video: PH Analyzing Special Types of Systems
Explore Learning
  1. Modeling Linear Systems - Activity A: Experiment with a system of two lines representing a cat‑and‑mouse chase.  Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real‑world meaning to slope, y‑intercept, and the intersection of lines.
  2. Solving Linear Systems by Graphing: Compare a system of equations in standard form or in slope‑intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
  3. Special Types of Solutions to Linear Systems: Compare a system of equations in standard form to its graph. Examine the graph and table of values. Determine the solutions to the system.
  4. Systems of Linear Equations - Activity A: Solve a system of linear equations by graphing and finding the intersection of the lines of the equations. Create a system of equations, examine its graph, matrix, and table of values, and determine the solution of the system.
Geogebra

 

Internet Sites
  1. Interactive Notes: Solving Systems by Graphing - lessons and practice problems at Regentsprep.org
  2. Notes: Solving Systems by Graphing - notes on graphing systems at Math For Morons
Tasks

 

Homework
  1. Casio Calculator Investigation: Graphing Systems (doc) | (pdf)
  2. Glencoe PWS (pdf)
  3. Glencoe SG (pdf)
Journal
  1. Systems of Equations: Summarize the three possible solutions to systems of linear equations. Give an example and characteristics of each.
Study Guide
  1. ExamView Quiz: Solving Systems by Graphing
  2. Prentice Hall Quiz
Other
HCPS 2002-