## Here at the NikAdas, we have been selling great soccer shoes to elevate your game !

A pair of shoes from the latest collection (2014-15) will cost \$300. This would make the total price for the pair y = 300x or -300x + y = 0

(Variables : y is the total price , x is the number of pairs you buy. Constant : \$300 is the price of a pair that you are going to buy)

A pair of shoes from the 2013 collection cost \$200. For these shoes, we have a membership that will give you amazing discounts on shoe customization, and on the shoe itself. Although necessary, a very reasonably priced membership with lots of benefits come your way. This membership costs only \$10, but it must be bought before the purchasing of your first pair. For the shoes, the total price comes to y = 200x + 10 or -200x + y -10 = 0

(Customizations include personalized colours, your name and jersey no.)

(Variables : Y is the total price, X is the number of pairs you buy. Constant's : \$200 is the price of one pair, \$10 is the one time must-buy price for the membership)

## Point Of Intersection or POI

This graph does show the POI,

I am also demonstrating below how to find the POI using the method of substitution

y = 300x

y = 200x +10

Let's convert this system so it is easier to work with

y = 300x

-200x + y = 10

Now that we know the value of y from the first equation, we can substitute it for the value of y in the second equation.

-200x + 300x = 10

100x = 10

100x/100 = 10/100

x = 1/10

Now we can substitute the value of x into the same equation to find the actual value of y

-200(1/10) + y = 10

-200/10 + y = 10

-20 + y = 10

y = 10 + 20

y = 30

Now that we know the value of both x and y intercept, we know that the POI is (1/10,30)

Although in these equations and this situation, the point of intersection doesn't really matter since we are selling shoes, and it would make a lot of sense to sell 1/10th of a shoe for \$30.

SUMMARY STATEMENT - Hence for \$30, you will get 1/10 of a pair of shoe

## Significance of this linear system

This linear system shows the way shop owners would work towards setting a price for their shoes, while bundling deals and memberships to go along with them. This situation is very realistic as I am trying to make the purchase of the older collection attractive to the buyers by offering a one time pay membership that he/she can use for as many pairs of shoes as they want. For the new collection, they price is higher and the total grows linearly with number of pairs bought in the form of direct variation as the line passes through the origin. The older collection also grows linearly with the number of pairs bought, but it is in the form of partial variation as there is charge of \$10 for the necessary membership before the shoes is even bought, and the line doesn't go through the origin. The graphs above also prove that this linear system can be solved graphically. These are the reasons that signify the solution of the linear system.