I posted this yesterday and no one bothered to check it, therefore Im posting it again, please check it this time.

Question

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?

???????????????

Answer 1

c) the solution for both p and d must be a positive integer.
Look at your second equation.
The left side is an even number, (anything multiplied by either 2 or 4 is even)
so you would have an even number equal to an odd number, which cannot be.
If you try to solve the system with the 2nd equation equal to 83, you would end up with a fraction as a solution. How can you have a fraction of a parrot or a fraction of a dog?

d) changing the 82 to 83 does not change the slope of the line, it simply raises the line parallel to itself.
The "nice" intersection point consisting of whole numbers now moves up as well, "wrecking" our nice numbers.

Answer 2

A)
Equation 1: 2p + 4d = 82
Equation 2: p + d = 24

Now you have to isolate a pronumeral from equation 2. For example:

Equation 3: d = 24 - p

Now you know what the value of 'd' is, you then substitute that into equation 1.

Which will equal:
2p + 4(24-p) = 82

2p + 96 - 4p = 82

-2p = -14

p = 7

Now that you know how many Parrots there were you simply just substitute into any of the equations.

Therefore d = 17 & p = 7

Note: if you have done simultaneous equations it would make more sense.

Hope this helps! :)