I am not a teacher myself, but the link to Mrs. Lazarus' page is https://schoolwires.henry.k12.ga.us/Domain/6540
Introduction
In this math project, we will be solving systems of equations using the three calculations elimination, substitution, and graphing while connecting it to real life. The purpose of this project is to show how systems of equations are necessary in real life problems and scenarios. One scenario includes where systems of equations is needed in cell phone planning. Within a family phone plan, the number of lines as well as the cost per data usage must be calculated.
One example includes Bell studying two large families with different cell phone plans in the same apartment building. In both families, household members live in different rooms, but all of them have the same cell phone plans. Family 1 pays $600 while Family 2 pays $1,000 and Bell is trying to figure out how many lines and the amount of data usage are being used in both families.
Task
The task is to solve the scenario by using the three calculations elimination, substitution, and graphing. Each calculation will have different steps and solutions; this is due to the goal of each one. Since this is systems of equations, the x and y will be the same in both equations/cell phone plans, but finding the x and y is the real challenge.
In elimination, the goal is to eliminate one of the variables to find the other variable, so the second variable can be used in one of the equations to find its counterpart. Your solution will be x and y (x,y)
In substitution, the goal is to solve one of the equations, for one of the variables. For example, with elimination you use the solved variable and substitute it for the chosen variable to find the other, and then check or solve for the 1st variable.
In graphing, the goal is to find the points that make up the solution by finding where the lines intersect. In some cases, the equations have to be analyzed and solved in order to find their y=mx + b.
Note* L= Number of lines stands for the x while d=amount of data stands for the y of the equations.
Process
Elimination: 20L + 2d= $600 30L + 5d= $1,000
First, we must find d(y), so we have to eliminate L(x). In order to do so, we have to make 20L and 30L the opposite of each other by multiplying them with outside numbers in parentheses, but all of the numbers inside the ( ) must be multiplied by the outside number as well. Next, we combine both d's and the total cost making them equal each other. Then, we divide the new d by its 4 and the total cost will be divided by the 4 as well, so you can find what d is equal to. Finally, plug the number into one of the problems to find L.
Substitution: 20L + 2d= $600 30L + 5d= $1,000 Note- the process will be a little different.
First, we make note that both of these equations are not in y=mx + b format or have a lonely y, so the process will be a bit different. In this case, we take 2d and rewrite the equation, 20L + 2d= $600 to isolate it. Then, we divide d by 2 and the rest of the equation by 2 as well to get our d/y.Finally, we substitute the new d into the other equation to try to solve for the other variable, but you will end with a no solution.
Graphing: 20L + 2d=$600 30L + 5d= $1,000
First, we take 20L and eliminate with its opposite(-20L) and $600 will be subtracted by negative 20L. If one thing happens to one side it happens to the other side. Next, we divide 2d by 2, and we also divide the 600 by two to get the new d/y, just like substitution. We do the same thing for the other equation, 30L + 5d=$1,000. Finally, we graph both until we find two points that intercept, which will be the answer.
Evaluation
The link for the class project rubric is:https://classroom.google.com/u/1/c/NTU0NDkwODMwMlpa/a/NTYxODA2OTA1Nlpa/details
Conclusion
In this project, I learned systems of equations are necessary
because they allow us to solve complex issues using simple method.
Mainly, this project is mainly based on standards that involved systems
of equations and graphing. Also, these standards are connected to previous
learning targets, which involved creating variables for equations discussed
in earlier units. Furthermore, I was able to connect this content to real life
situations such as the cell phone industry.
While doing research, I discovered how challenging cell
phone planning could be for people. There is a great demand for the use
of systems of equations in cell phones especially for family plans pertaining
to data usage, number of lines on the cell phone plan as well as the company
providing the service. I enjoyed researching about cell phones plans that
allowed me to realize how wonderful math is in any situation. However, it was
still a bit difficult finding the second variable for the equations, and identifying
what technology to utilize from many choices, and learning how cell phone
plans can be a bit complex when it to data usage.
Finally, there were some mistakes I realized while completing this project.
When I was solving equations, I thought everything was right until doubling
Checking and realizing when subtracting I put in the wrong number. This caused
my equations to be incorrect, and it made me realized that one wrong turn can
mislead a person for a long time. If I were given another opportunity to do this,
I would manage my time better and really look a to make sure the variables are correct.
Credits
For this project, I give credit to my family. They really helped with mapping out the design for the model of the project. Also, I utilized www.purplemath.com/modules/systlin4.htm to research information and instructions for what do in substitution if one of equations does not look like y=mx + b. Also, I thank my teacher, Mrs. Lazarus, for teaching the lesson and helping me when I needed assistance in class. Finally, for the content/ information on the cell phone planning I give credit to various websites.