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Systems of Linear Equations, Coursework Example

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For a long time now, it has become a habit for me to take a cup of ice cream and a bottle of soda every day. My craving for ice cream makes me window shop around shops just to check on any ice cream. On Saturday s, i have a favourite spot where i get an offer because i get both the ice cream and soda for only $1. On Sundays, my friends and i meet up for a movie and i always order for the two cups of ice cream and a bottle of soda for $4. Putting this into an equation;

Let x be the number of cups of ice cream

y be the number of bottles

On Saturday, the equation would be x+y=1

Sunday’s equation is 2x+y=4

To solve these two equations so that we can determine the cost of a cup of ice cream and a bottle of soda, the following procedure would be followed:-

  • Choose the best method to use and i have settled on substitution method
  • Substitute one equation into the other such that the second equation is described in terms of the first equation.
  1. i) x+y=1
  2. ii) 2x+y=4

Use x+y=1

x=1-y

Substitute in equation ii

2(1-y)+y=4

2-2y+y=4

Put like terms together

-2y+y=4-2

-y=2

Y=-2

If y is 2 then

X+y=1

X+(-2)= 1

X=1+2

X=3

If x= 3 and y=-2, this therefore means that a cup of ice cream costs $3 while a bottle of soda costs $2. The negative sign on the price of the soda only means that the price is $2 but it is offered as a discount because the main thing on sale here is ice cream.

This is a consistent equation because the two equations have a common solution which is x=3 and y=-2.

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