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.
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! :)
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