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equation

by rupsk » Thu Jul 28, 2011 8:07 am
How many positive integer solutions for are there satisfying the equations?

x+y=p
x-y=p+2k+1

A. Infinite number of solutions exist


B. Finite number of solutions exist but more than one


C. Exactly one solution exists

D. Exactly two solutions exist

E. No solution exists
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by Frankenstein » Thu Jul 28, 2011 9:19 am
Hi,
From the two equations, we get 2x = 2(p+k)+1 and 2y = -(2k+1). With no constraints on p and k, x and y can have infinite positive integral solutions(A). If only, you have mentioned p and k are integers, then the answer is E because LHS is even and RHS is odd. If you have said k is positive, then answer is again E. So, we can have different answers depending on the constraints. So, I guess the question must be having some constraints. Otherwise, the answer is A.
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by rupsk » Thu Jul 28, 2011 9:21 am
Yes i missed out on the constraint it says p and k are integer.
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by Frankenstein » Thu Jul 28, 2011 9:23 am
rupsk wrote:Yes i missed out on the constraint it says p and k are integer.
Well then the answer should be E as I have explained above. I hope it is clear.
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