This presentation provides students with opportunities to engage, explore, apply, and connect the algebraic concept of systems of linear equations by using cell phone plans.  By determining the intersection point of two plans, students can make informed decisions.  The learning concept will extend into recognizing that in any comparison of systems of linear equations, there are only three possible results: one solution, no solution, or infinite solutions.
(All images from a purchased clipart collection.)
Mathematics 10 Foundations and Pre-calculus
Outcome 10: Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
Learning Concept 2: We can determine intersection points graphically and mathematically.

How Would You Choose a New Cell Phone?
What cell phone features are most important to you?  Are they the same as your classmates? When comparing cell phones, the comparison is largely qualitative and some features are prioritized over others so choosing a cell is subjective.  However, when comparing cell phone plans, we can use algebra to assist us in quantitative comparisons that are very objective.
Monthly Cell Phone Plan A (Black Line)
Our first cell phone starts at $30 dollars for 200 minutes and charges $0.25 for every minute above.
Monthly Cell Phone Plan B (Red Line)
Starts at $25 dollars for 200 minutes and charges $0.30 for every minute above.

Cell Phone Plans as
Systems of
Linear Equations
Nancy Carswell
EDIM508 Digital Media in the Classroom
We can see the intersection point is at 100 minutes and $55.00.  At this point Plan A becomes cheaper than Plan B.
If you know you use well under 100 minutes a month, Plan B is the way to go.
If you know you use well over 100 minutes a month, Plan A is the way to go.
But what happens if you use around a 100 minutes a month?  The smart thing to do would be to go with Plan B so that if you are under 100 minutes, you will save.  If you find yourself consistently over 100 minutes, then switch to Plan A.
Operation Algebra: Introduction to Linear Systems. Noodle Logic , 2000. Full Video. 23 March 2011. <http://www.discoveryeducation.com/>.
One Solution
We could see from our formulas in slope intercept form, y = mx + b, that our slopes were different, Plan A 0.25 and Plan B 0.30.  Different slopes indicate the lines will have an intersection point.  This video shows us another system of linear equations with One Solution.

Operation Algebra: Introduction to Linear Systems. Noodle Logic , 2000. Full Video. 23 March 2011. <http://www.discoveryeducation.com/>.
Operation Algebra: Introduction to Linear Systems. Noodle Logic , 2000. Full Video. 23 March 2011. <http://www.discoveryeducation.com/>.
Operation Algebra: Introduction to Linear Systems. Noodle Logic , 2000. Full Video. 23 March 2011. <http://www.discoveryeducation.com/>.
No Solution
What would our lines look like though if Plan A was y = 0.25x + 30 and Plan C was y = 0.25x + 25?  Here our slopes are the same so the lines are parallel.  This video shows another system of linear equations with No Solution.

Infinite Solutions
What would happen if our Plan A was y = 0.30x + 30 and Plan D was 2y = 0.60x + 60? Do you see a common factor of 2 in Plan D?  Factoring this linear equation leaves us with the same linear equation as Plan A.  This video shows us another system of linear equations with Infinite Solutions.

Review
This video provides a review of our three possibilities for any system of two linear equations: one solution when the lines intersect at a point, no solution when the lines are parallel, and infinite solutions when the lines are coincidental.  

Application
Visit http://fooplot.com/ and generate a graph for our cell phone plans that show No Solution for Plan A y = 0.25x + 30 and Plan C y = 0.25x + 25.  Which is the cheaper plan?
Generate a graph for the following cell phone plans given in slope-point form: Plan E (y - 40) = 0.20(x - 25) and Plan F
(y - 28) = 0.35(x - 40).  Before graphing, predict One Solution, No Solution, or Infinite Solutions.
Final Connection
Are you knowledgeable on the true costs of using credit?  Credit card companies in Canada added "minimum payment warnings" in the fall of 2010.  Imagine you bought a $500 computer.  If you just make minimum payments of $15, how long do you think it would take to pay off this debt if the interest rate was 19.5%?  Would you be surprised to learn that it would take 10 years and 5 months?  Do you think credit card companies should give minimum payment warnings as written statements or as visual graphs?  Explain.
Reflection
Do you use proper cell phone etiquette?
This song by the Arrogant Worms
reminds us the respectful thing to do
is to give people present priority
over people on the phone.
Lyrics available at http://www.arrogantworms.com/music/cellphone-vigilante/.
YouTube - Arrogant Worms - Cellphone Vigilante. (n.d.). YouTube - Broadcast Yourself. Retrieved March 30, 2011, from http://www.youtube.com/watch?v=iAck24Nzh-g