A Linear System Flyer

By: Sayoohn Lingarasan

Statement of Situation: Comparison of Cellphone Plans

Two different cellphone companies have released new plans for the holidays.

Info-tech charges an activation fee of $60 and $40 for every month the plan is used.

Net-link charges no activation fee and $50 for every month the plan is used.

Identification and Classification of Variables

On the table:
  • Let "x" represent the number of months the plan is used.
  • Let "y" represent the cost of the plan.

In the equation:
  • m= Slope
  • b= Y- Intercept

Table of Values for Info-tech Company

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y=40x + 60

Table of Values for Net-link Company

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Graph Showing Linear Relation and Point of Intersection

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Graphic Solution for Point of Intersection

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Algebraic Solution for Point of Intersection




Applying "x" (6) to the "y=mx+b" Equations






Therefore, the point of Intersection is (6,300) and the costs in 6 months is $300.

Significance of the Solution to this Linear System

The solution of this linear system is significant consequent to the fact that the point of intersection displays the better choice in 2 linear relations. In relation to the context of the authentic real-life situation, this particular solution makes sense. To clarify, the point of intersection expresses the time, in this case the amount of months, when the costs for both plans will be equal. This solution is significant because it gives one the ability to establish the best plan that they could pick and under what circumstances. Furthermore, one can now (with evidence) state that Net-link cellphone company is the better option if one uses the plan for up to 6 months. If one will use the plan for exactly 6 months, the choice in plan is not significant as Net-link's fees will steadily increase and then equal that of Info-tech's. However, if one decides to use the plan for above 6 months, the accurately better option would be to choose the Info-tech cellphone company's plan. This is also because the slope in the equation for Net-link cellphone company is greater than that of Info-tech cellphone company's. In conclusion, this is the significance of the solution to this linear system.

A Summary Statement

To finalize, the costs of both Info-tech and Net-link cellphone company plans will both be $300 in 6 months.