Question

You go to Verizon to buy a new Iphone. You expect to pay $800 for a new phone and $70 a month. But this is not the only option.

Option 1: Pay $800 for the phone and $70 a month. Option 2: Pay $200 for the phone and $90 a month.

Clearly if you stay on this plan for only a short time option 2 is cheaper. you stay on the plan long enough, option 1 is cheaper. In order to help you chose which option to take, you decide to compute the number of months when both options cost the same total amount. On month zero option 1 costs $800, on month one it costs $870,...Starting with y=mx+b, write the system of equations:

a) Equation for option 1:

Equation for option 2:

b) Solve the system of equations

c) Demonstrate that there is only one solution to the system of equations.

Answer 1

Let the equation be y=mx+c, where

y=cost of iphone after x months of purchase(in $)

x=the number of months after the purchase

c=Initial cost in $

m=cost per month in $

a)

Option 1	Option 2
The equation is y=70x+800	The equation is y=90x+200

b)

We have the two equations as:

y=70x+800..............................................(i)

y=90x+200..............................................(ii)

From (i) and (ii)

70x+800=90x+200

=> 20x=600

=> x=30

Put x=30 in (ii)

y=90(30)+200

=> y=2900

Hence the solution is (30,2900)

c)

y=70x+800..............................................(i)

y=90x+200..............................................(ii)

The above system of linear equations is system of linear equations in two variables which represents two straight lines. In a plane two straight lines either intersect at one point (has only one solution) or both coincide (intersect at infinite number of points=> infinite number of solutions)

Both lines coincide if they have same value of slope (i.e. m) and in all other they intersect at one point.
Here, we have the values of m as 70 and 90 i.e. not equal. Hence, The given system of equations has only one solution

*Please do rate my answer.