Did I do this correct? Can someone help me fix this please?

For the final project, you will do all of the following steps:

Describe another setting in which a systems of equations approach would be useful.

Present data for an application of your choice. (This topic was submitted in your Module7 Proposal.) Be sure to cite any sources if you use outside references for ideas or data.

Write a linear equation of the form y₁= mx + b for your first set of data. Graph this equation on the xy-plane and label it as y₁. You may use Excel to graph, search online for graph paper options to use, or use the 'draw' tools in Word to plot your lines (Graphsketch.com is resource which you may find helpful when constructing your graph.)Also, be sure to include a title on the graph and labels on the x- and y-axes.

Write a linear equation of the form y₂= mx + b for the other equation in your system. Graph this equation on the same graph. You will now have two lines on the same graph. These should intersect.

Find the point of intersection for y₁and y₂algebraically (by setting the equations equal to each other and solving). Show your work and also plot this point on the graph.

Analyze the data and explain what the intersection means, in terms of the problem. Is there a 'best' solution to your problem? If so, under what conditions?

Conclude your project with a short summary of what you learned.

Almost any situation where there is an unknown quantity can be represented by a system of equations , like figuring out income over time, calculating mileage rates, or predicting profit. Suppose there is a problem situation that is completely related to our real life. Anne is trying to choose between two phone plans. The first plan, with Vendafone, costs $20 per month, with calls costing an additional 25 cents per minute. The second company, Sellnet, charges $40 per month, but calls cost only 8 cents per minute. Which should she choose? You should see that Anne's choice will depend upon how many minutes of calls she expects to use each month. We start by writing two equations for the cost in dollars in terms of the minutes used. Since the number of minutes is the independent variable, it will be our x. Cost is dependent on minutes - the cost per month is the dependent variable and will be assigned y.

For Vendafone: y = 0.25x + 20

For Sellnet: y = 0.08x + 40

The line for Vendafone has an intercept of 20 and a slope of 0.25. The Sellnet line has an intercept of 40 and a slope of 0.08 (which is roughly a third of the Vendafone line's slope). In order to help Anne decide which to choose, we'll find where the two lines cross, by solving the two equations as a system. So if Anne uses 117.65 minutes a month (although she can't really do exactly that, because phone plans only count whole numbers of minutes), the phone plans will cost the same. Now we need to look at the graph to see which plan is better if she uses more minutes than that, and which plan is better if she uses fewer. You can see that the Vendafone plan costs more when she uses more minutes, and the Sellnet plan costs more with fewer minutes.

So, if Anne will use 117 minutes or less every month she should choose Vendafone. If she plans on using 118 or more minutes she should choose Sellnet.