Algebra Units Systems of Equations
Systems of Linear Equations

 Objective 1: Solve a system of linear equations by graphing. 7.1 Test to see if an ordered pair is a solution to a system of linear equations. 7.1 Use a graph to find the solution to a linear system.
 Objective 2: Solve a system of linear equations using substitution 7.2 Isolate one variable in one equation of a system of equations 7.2 Substitute expressions for variables to simplify systems of equations
 Objective 3: Solve a system of linear equations using elimination (also called linear combinations) 7.3 Rewrite equations to a consistent format 7.3 Use the properties of equations to rewrite equations 7.3 Add and subtract polynomials to simplify and solve systems of equations
 Objective 5: Set up a system of linear equations to model real-world problems 7.4 Write a system of linear equations from a word problem 7.4 Solve a system of linear equations using all three methods (graphing, elimination, substitution) 7.4 Review a system of linear equations, explain how one method may be better (or simpler) for solving a system than another. Compare methods for solving systems of equations.
 Objective 6: Identify a system of linear equation as having one solution, no solution, or infinitely many solutions. 7.5 Use properties of a linear equation to identify special case solutions of linear systems 7.5 Review the steps of solving linear systems to identify errors
 Key Concepts/Vocabulary Concept:1. Linear systems Concept:2. Solutions of a linear system Concept:3. Polynomials Concept:4. linear combinaations Concept:5. slope-intercept form of an a linear equation y=mx + b

## Skills Quizzes : Systems of Linear Equations

Quiz Name Skill Assessed Practice File Passing Grade Notes
Graphing Solve systems of equations by graphing; check the solution See homework assignments for practice problems 3 out of 4
Substitution Solve systems of equations using the substitution method; check the solution. See homework assignments for practice problems 3 out of 4
Linear Combinations Solve systems of equations using linear combinations; this includes adding, subtracting, multiplication, division; check the solution. See homework assignments for practice problems 3 out of 4
Writing Systems of Equations Write a system of equations to model a problem; then solve the system and check the solution. 5 out of 6
Writing Systems of Equations Write a system of equations to model a problem; then solve the system and check the solution.
Sample: The difference of George's age and Madison's age is 9 years. The sum of 6 times George's age and 5 times Madison's age is 153. How old is each?
Practice problem sets (PDF) 3 out of 3 Practice problem set solutions (PDF)
Sample Word Problems For each of these word problems, students should be able to:
• Write a system of equations that models the propblem
• Choose an appropriate method for solving the system - graphing, substitution, linear combinations
• Solve the system (for all variables)
• Check the solution (in all equations) algebraically

 Samantha has \$3.40 in dimes and quarters. The number of dimes is 8 less than the number of quarters. How many coins of each type does she have? A piggy bank has \$4.30 in dimes and quarters. If the number of dimes is 7 more than 2 times the number of quarters, how many coins of each type are in the piggy bank? George's age is 5 times Kendell's age. The sum of their ages is 48. Find the age of each. The difference of Jimmy's age and Linda's age is 10 years. The sum of 5 times Jimmy's age and 4 times Linda's age is 104. How old is each? There were 235 people at a movie to raise funds for the drama club. Admision was \$8.00 for each adult and \$4.00 for each student. The total receipts for all tickets was \$1504.00. How many adults and how many students attended? The length of a rectangle is 11 m less than 5 times the width. The perimeter is 434 m. Find the length and width of the rectangle. George scored 13 more points than twice as many as Roy did. Their combined score was 40 points. How many points did each score? The difference of Jen's age and Mark's age is 6 years. The sum of 4 times Jen's age and 3 times Mark's age is 108. How old is each?

Content Covered
Text Book Algebra I
• Chapter 7

### Assignments

To Review all topics from this unit:

Chapter 7 Chapter Review
• Read the chapter review pages 440-442
• Complete problems from 7-1 1-6
• Complete problems from 7-2 7-12
• Complete problems from 7-3 13-18
• Complete problems from 7-4 19-20
• Complete problems from 7-5 21-26

Chapter 7 Chapter Test
• Do problems 1-24 page 443
• Complete problem 31 page 443

Standardized Test Practice
• Complete problems page 444 1-10
• Complete problems page 445 13 - 16

Summary and Reminders

Reminders
• Students should keep up with their homework - it is much easier to keep up than to catch up
• If you do not perform well on a skills quiz, seek extra help and practice and re-take the quiz as soon as possible
• Do not wait until the last moment to complete assignments - start early, so if you have questions you have time to ask them and have them answered before assignments are due.
 Student Handouts/Resources The Scrapbook Project The project for this unit is a scrap book page which should contain the following : Notes about solving systems of equations using the graphing method; and one or more examples. Notes about solving systems of equations using the substitution method; and one or more examples. Notes about solving systems of equations using linear combinations (also know as the elimination method).; and one or more examples. Notes about writing a system of equations from word problems; and one or more examples. Notes about which method to use or how to choose a method for solving a system of equations. Solutions to the problems selected for the Scrapbook project are in the file ScrapbookProblems.pdf. The main solutions are on the first page, but there are some addition problems that we worked out in class. These are the answers only - not the complete solutions. You should write out the complete solutions and then check your answers here. Problem sets will be handed out in class to supplement the assignments from the textbook Online resources will be posted to supplement content material / presentations

 April 2012 Computer Lab April 10, 2012 Solving systems of Equations by Elimination (also called linear combinations) Complete the practice problems in this Solving Systems of Equations by Substitution PowerPoint show. View a demonstration Solving a system with two equations and try the practice problems. Review and Practice: Linear Combintions View a deomonstration of Solving a system with three equations and try the practice problems. Complete the extra examples available on Classzone.com Additional References - for solving systems by elimination PurpleMath.com The Math Dude solves systems of equations

March 2012 Go to the Flip Chart page to see what information should be included on each page.

Flip-charts are due on the day of the unit test next week. If you have any questions be sure to ask. The flip-charts represnt ten percent of your quarter 3 grade. You enrolled in Quia in the beginning of the year, creating your own userid and password. I have acces to your first name, last name, and e-mail address that you used when you registered but not your userid or password. If you need to recreate a free account, after you register you will need to enter a class code.

Be sure to log into Quia when you are doing any activities so you will get credit.

Class: Algebra A-Block

Code: PTMFBK476

## How to register

Step 2. Now, click the area labeled Students. When the next page appears, enter your username and password if you already have a Quia account. If you do not have an account, click the link Create my free account. Fill out the form that appears. Select "Student" as the account type. When you are done, press the Create my account button.
Step 3. You should now be in the Student Zone. Type in the class code FGAMK879 in the text field and press the Add class button. Now you're done!
Now that you have registered for the course, you can view your class web page, take quizzes, view your quiz results, view time spent on Quia activities, and read your instructor's feedback from your Quia account.
Follow these steps to view your results:
1. Log in to your account. (Remember, go to the Quia Web home page at http://www.quia.com/web and click the area labeled Students.)
2. Click on the class name. Data Analysys

## GeoGebra

• Tuesday you used GeoGebra to model and solve problems. You can find free downloads of the software at GeoGebra.org. If you do not want to download it or have a computer platform that does not support it, you can use the versions that works within the web browser.

## Additional Online Resources

Classses that did not use GeoGebra used these online resources to complete the same problem set that you were given. You can use these tools to review information about data analysis or use these tools to help you with your homework or other assignments.
• Use the Box and Whisker Plot Activity at Classzone to practice each step of creating a box and whisker plot.

• Use the online tools Box Plot and Histogram to create graphs. Read through the examples that are provided, then use the tools to solve problems from the handout.

• Use the interactive tools at Shodor.org to create Stem and Leaf plotd to solve the problems from the handout.