The south edmonton pet shop has several parrots and dogs for sale. There are a total of 24 heads and 82 legs in the display cages.
A) Write a system of linear equations to represent the number of parrots, p, and the number of dogs, d, for sale.
p+d = 24
2p+4d = 82
B) Determine the solution to this system graphically(done it)
c)Explain why this system of linear equations would have no solution if the total number of legs is changed from 82 to 83?
Cause it wouldnt equal up with eachother? no sure how to rephrase this into a better answer.
D) Why is your answer to part C not related to the slopes of the two lines?
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C) In this system of linear equations, the number of heads and legs are used to represent the number of parrots and dogs for sale. The total number of heads is represented by the equation p + d = 24, where p is the number of parrots and d is the number of dogs. The total number of legs is represented by the equation 2p + 4d = 82, where 2p represents the number of legs from parrots (since each parrot has 2 legs) and 4d represents the number of legs from dogs (since each dog has 4 legs).
If the total number of legs is changed from 82 to 83, the system of equations would have no solution. This is because the number of legs cannot be divided evenly among parrots and dogs. Since parrots have 2 legs each and dogs have 4 legs each, it is not possible to have a total of 83 legs with only parrots and dogs. This means that no combination of parrots and dogs can be found to satisfy the new total number of legs.
D) The answer to part C is not related to the slopes of the two lines because in this problem, we are not comparing the rates of change (slopes) of the two equations. Instead, we are looking at the specific values that satisfy both equations simultaneously. When we talk about "no solution" in this context, it means that there are no values of p and d that can satisfy both equations at the same time, regardless of the slopes of the lines represented by those equations. The slopes of the lines only indicate the rate of change, not the specific values of p and d.