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## Please read the information in the above prompt and note the topics covered in w

Please read the information in the above prompt and note the topics covered in week 4 as well as instructions given relating to your Initial Post.  I have videos on each of the week 4 topics in the announcements for additional help.
I am getting us started by giving you an example solved using both the Substitution and Elimination methods.
I hope you find it helpful.
EXAMPLE PROBLEM
I thought I would show you an example solving the following system of equations using first the Substitution Method and then the Elimination Method:
2x+y=8 x-y=1
First, I will use the Substitution Method.  Solving for x in the second equation yields x=1+y.  Now, substitute this into the first equation in place of x.  2(1+y) + y=8 We must now simplify this equation.  2+2y+y=8 After combining like terms on the left we have 2+3y=8 Now solve for y by subtracting 2 on both sides.  3y=6 Now divide both sides by 3, which gives y=2.   This can be substituted into either equation to solve for x.  In the second equation, x-2=1 Now add 2 to both sides which gives x=3.  The solution to the system is x=3, y=2 which gives the point represented by the ordered pair (3,2).
Next, I will solve this system of equations by the Elimination Method which is sometimes called the Addition Method. This method calls for us to line up like terms beneath one another, which is already done in our example.  We want to be able to add the two equations and eliminate one of the variables.  Our example is set up to eliminate y.  If this was not the case, you would need to multiply one of the equations by the necessary constant to make this happen. 2x+y=8   x -y=1 ——— 3x    = 9     This is found by adding the two equations.  Now divide both sides by 3, to get x=3.  Substitute 3 in place of x in either equation to solve for y.  I will use the first equation.  2(3) + y=8   now 6+y=8   next we subtract 6 on both sides which gives y=2.  The solution is (3,2)
You will get practice with both of these methods this week as well as solving a system using the Graphing Method.  Let us know which of the 3 methods you like best and why.
Now let’s get started:
**Post a problem and show your step-by-step solution using one of the three methods. Don’t forget to do a check. Put your solution into your original problem. Does it work?

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## Hi Everyone, This session the Week 4 Presentation involves solving a System of E

Hi Everyone,
This session the Week 4 Presentation involves solving a System of Equations using two different methods.  You are given a Template with the Slides youare supposed to use for your PowerPoint, and YOU will supply the information on the slides as well as the audio explanation of your work.
Please read the Instructions for the Presentation carefully and check the Rubric to see how your grade is to be calculated.  I will go over all of this on Monday in our Virtual Live Lecture.
The Presentation is the last item in Week 4 in Modules. This Presentation is worth 50 points.  Please submit it by no later than 2/5/23.
Basically, you are to choose two of the methods used to solve a System of Equations and demonstrate those Methods as you solve the following system:
5x + 3y = -7
6x – 7y = -19
Be sure to show your work for each method and explain each step of the process.  If you should choose Graphing as one of your methods, you cannot just show the graphs.  You need to show your method and calculations used to graph each line and then how you got the solution.
For any method you choose, be sure to explain your steps in writing as well as verbally in the narration.
In the Presentation Instructions, you are given a variety of ways to supply the audio and links with information on each.  Be sure to use one of these methods.  You are also given a few questions to answer at the end of the presentation.  Be sure to answer these questions as it is part of your grade!

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## Identify the extraneous solution and explain how it was determined to be extraneous.

Scenario
You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram attached below:

Assessment Instructions
SHOW and EXPLAIN all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.
Part 1: Find the total area of flower bed.
Part 2: Write the area of the flower bed as an equation using multiplication of two binomials.
Part 3: Solve your equation from Part 2.
Part 4: Identify the extraneous solution and explain how it was determined to be extraneous.
Part 5: Find the width of the part of the flower bed with the daisies.

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## Identify the slope and y-intercept of the equation in the graph.

The graph attached below is provided by a ride-sharing service in your area showing the cost, in dollars, of a ride by the mile.

Assessment Instructions
Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.
Part 1: Calculate the base fee (in dollars) charged by the ride-share service.
Part 2: Calculate the rate of increase in cost in dollars per mile.
Part 3: Identify the slope and y-intercept of the equation in the graph.
Part 4: Write the slope-intercept equation of the line in the graph.
Part 5: Use your equation from part 4 to extrapolate the cost of a 30-mile ride.