Intro W6

• 1. Current Page: Intro W6 (1 of 14)
  2. Resources W6 (2 of 14)
  3. TN W6, Assignment (3 of 14)
  4. 5.1 Video Lesson, Assignment (4 of 14)
  5. 5.2 Video Lesson, Assignment (5 of 14)
  6. 5.3 Video Lesson, Assignment (6 of 14)
  7. 5.4 Video Lesson, Assignment (7 of 14)
  8. 5.2 - 5.3 Practice, Assignment (8 of 14)
  9. 5.4 Practice, Assignment (9 of 14)
  10. 5.5 Practice, Assignment (10 of 14)
  11. 5.6 Practice, Assignment (11 of 14)
  12. Discussion - Collaboration Setup (12 of 14)
  13. Collaboration 1, Assignment (13 of 14)
  14. Outro W6 (14 of 14)

        Intro W6

  •  Objectives

    1. An architect designing a home may have restrictions on both the area and perimeter of the windows because of energy and structural concerns. The length and width chosen for each window would have to satisfy two equations: one for the area and the other for the perimeter. Similarly, a banker may have a fixed amount of money to put into two investment funds. A restaurant owner may want to increase profits, but in order to do that he will need to hire more staff. A job applicant may compare salary and costs of commuting for two job offers.

       In this chapter, we will look at methods to solve situations like these using equations with two variables.

    3. The sections for this week are:
       • 5.2 Solving Systems of Equations by Substitution
       • 5.3 Solve Systems of Equations by Elimination
       • 5.4 Solve Applications with Systems of Equations
       • 5.5 Solve Mixture Applications with Systems of Equations
       • 5.6 Graphing Systems of Linear Inequalities

   

   Intro and Learning Objectives (click on all tabs to see all sections)

  • • 5.2
    • 5.3
    • 5.4
    • 5.5
    • 5.6

     Learning Outcomes

    In this section, you will:

    • Solve a system of equations by substitution
    • Solve applications of systems of equations by substitution

     Intro

    Solving systems of linear equations by graphing is a good way to visualize the types of solutions that may result. However, there are many cases where solving a system by graphing is inconvenient or imprecise. If the graphs extend beyond the small grid with x and y both between −10 and 10, graphing the lines may be cumbersome. And if the solutions to the system are not integers, it can be hard to read their values precisely from a graph.

    In this section, we will solve systems of linear equations by the substitution method.

     Learning Outcomes

    In this section, you will:

    • Solve a system of equations by elimination
    • Solve applications of systems of equations by elimination
    • Choose the most convenient method to solve a system of linear equations

     Intro

    We have solved systems of linear equations by graphing and by substitution. Graphing works well when the variable coefficients are small and the solution has integer values. Substitution works well when we can easily solve one equation for one of the variables and not have too many fractions in the resulting expression.

    The third method of solving systems of linear equations is called the Elimination Method. When we solved a system by substitution, we started with two equations and two variables and reduced it to one equation with one variable. This is what we’ll do with the elimination method, too, but we’ll have a different way to get there.

     Learning Outcomes

    In this section, you will:

    • Translate to a system of equations
    • Solve direct translation applications
    • Solve geometry applications
    • Solve uniform motion applications

     Intro

    Previously in this chapter we solved several applications with systems of linear equations. In this section, we’ll look at some specific types of applications that relate two quantities. We’ll translate the words into linear equations, decide which is the most convenient method to use, and then solve them.

    We will use our Problem Solving Strategy for Systems of Linear Equations.

     Learning Outcomes

    In this section, you will:

    • Solve mixture applications
    • Solve interest applications

     Intro

    When we solved mixture applications with coins and tickets earlier, we started by creating a table so we could organize the information. For a coin example with nickels and dimes, the table looked like this:

    

    Using one variable meant that we had to relate the number of nickels and the number of dimes. We had to decide if we were going to let n be the number of nickels and then write the number of dimes in terms of n, or if we would let d be the number of dimes and write the number of nickels in terms of d.

    Now that we know how to solve systems of equations with two variables, we’ll just let n be the number of nickels and d be the number of dimes. We’ll write one equation based on the total value column, like we did before, and the other equation will come from the number column.

    For the first example, we’ll do a ticket problem where the ticket prices are in whole dollars, so we won’t need to use decimals just yet.

     Learning Outcomes

    In this section, you will:

    • Determine whether an ordered pair is a solution of a system of linear inequalities
    • Solve a system of linear inequalities by graphing
    • Solve applications of systems of inequalities

     Intro

    Two or more linear inequalities grouped together form a system of linear inequalities.

    A system of linear inequalities looks like a system of linear equations, but it has inequalities instead of equations. A system of two linear inequalities is shown below.

    $x+4y\ge0$

    $3x-2y<12$

    To solve a system of linear inequalities, we will find values of the variables that are solutions to both inequalities. We solve the system by using the graphs of each inequality and show the solution as a graph. We will find the region on the plane that contains all ordered pairs (x,y) that make both inequalities true.

     Readings

    1. Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
    2. Videos: Watch all the videos from "Resources W6"

     Assignments

    • Take Notes Week6         Due Friday night.
      

    Directions

    •  Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:

    • • Your name
      • The name of the section
      • Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
      • Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
      • You have to solve ALL "Try It" exercises.

    After you complete your notes you have to submit them. See Take Notes Methods. 

     

    • Video quizzes Week 6          Due Saturday night 11:59pm.

    Directions

    • To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.

     

    • Homework Week  6              Due Sunday night 11:59pm.
    •  

    Directions

    • There are 4 Practice Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.

     

           Discussion - Collaboration Setup             1st post due Thursday 03/10

                                                             2nd post due Monday 03/14

     

    • Collaboration 1 Assignment                         Due  Sunday 03/13                                                                                                                After you have gmail and Google drive set up, you are ready to start this assignment. Each one of you is part of a group with 10-12 students. Each group has a Google page which is in the cloud. You have to access this page and follow the instructions to complete the tasks. To access the page click on "Collaborations" link in the left Navigation menu. Either you have direct access to the page, or you have to ask my permission to get access. 

    Directions

    This assignment is a discussion in which you have to talk about setting up a gmail, Google drive, and integration in Canvas. This are tools you need to start the Collaboration assignment. 

    This discussion is also the place where you can ask and get help for Collaboration assignments.

  The due dates for assignments are Friday, Saturday, and Sunday.

  However, you can submit them until Tuesday night next week.

  A 5% per day penalty applies for late work if you'll do it until Tuesday night.