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# Consistent and Inconsistent Linear Systems

## Systems with parallel or intersecting lines

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AT&T & Verizon - Same Cost?
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## Real World Applications – Algebra I

### Topic

Comparing Iphone Plans – Same Cost?

### Student Exploration

In this concept, you learned how to differentiate between a consistent and inconsistent system of linear equations. In this demonstration, you will see how an inconsistent system of equations is represented between the most popular cell phone and cell phone carriers of 2012 – AT&T Wireless and Verizon Wireless. Both service providers carry very similar phones, such as the Iphone 4S. As of July 2012, their competitive prices are actually quite similar – so similar that the relationship between the two wireless providers could represent an inconsistent system of linear equations.

Let’s take a look at AT&T Wireless first. An Iphone 4S costs $199. The unlimited talk plan costs$70/month, “unlimited” data (up to 3 gigabytes) costs $30/month, and the one-time activation fee costs$36.

Now let’s look at Verizon Wireless. An Iphone 4S also costs $199. The unlimited talk and text plan costs$60/month, which also includes up to 2 gigabytes of data. There is also a monthly fee of $40 for mandatory access to the network. The one-time activation fee costs$35.

If we were to make an equation for each cell phone provider, we have to identify the two unknowns. Let x\begin{align*}x\end{align*} represent the number of months you would use this plan, and let y\begin{align*}y\end{align*} represent the total cost. The equation for AT&T Wireless would be y=(70+30)x+36\begin{align*}y = (70+30)x + 36\end{align*}. The equation for Verizon Wireless would be y=(60+40)x+35\begin{align*}y = (60+40)x + 35\end{align*}. If we simplified both of these equations, we would have:

AT&T: y=100x+36\begin{align*}y = 100x + 36\end{align*}

Verizon: y=100x+35\begin{align*}y = 100x + 35\end{align*}

Does this system of equations represent a consistent or inconsistent system?

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