What is the maximum number of possible solutions for the system shown below?

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What is the maximum number of possible solutions for the system shown below?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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the choices are 1,2,3, and 4
y^2=36-x^2--(1) Sub (1) into x^2-4y^2=64 x^2-4(36-x^2)=64 x^2-144+4x^2=64 5x^2=64+144 5x^2=208 x=(+/- sqrt 208/5) and then continue to sub in from here to find the number of solution

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what would the final answer be in that case? @amstro
i will figure it out afterwards, i just need an answer quickly, please help
thank you :)
Hint: |dw:1358003669486:dw|
@erin512 Im so sorry! There is no solution as y^2=36-(+/- sqrt 208/5)^2--> y^2=36-(208/5) hence there will be no solution as the eqn is undefined
no problem! thank you though :) its a multiple choice question and there options are 1,2,3 or 4 solutions, so i'm not sure which it correct :(
@erin512 @amstro Without solving the equations, there is a maximum _possible_ solution of 4, since they are both second degree. The actual solution is zero, still < maximum possible. The question is very vague. I would put parameters a,b,c,d instead of numbers for the purpose of the question, such as x^2-ay^2=64...
@mathmate thank you so much :) so do you think 4 would be the correct answer in this case?
Agree.
thank you so much :) i really appreciate it
you're welcome! :)

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