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erin512

  • 3 years ago

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

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  1. erin512
    • 3 years ago
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  2. erin512
    • 3 years ago
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    the choices are 1,2,3, and 4

  3. amstro
    • 3 years ago
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    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

  4. erin512
    • 3 years ago
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    what would the final answer be in that case? @amstro

  5. erin512
    • 3 years ago
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    i will figure it out afterwards, i just need an answer quickly, please help

  6. erin512
    • 3 years ago
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    thank you :)

  7. mathmate
    • 3 years ago
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    Hint: |dw:1358003669486:dw|

  8. amstro
    • 3 years ago
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    @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

  9. erin512
    • 3 years ago
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    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 :(

  10. erin512
    • 3 years ago
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    @amstro

  11. mathmate
    • 3 years ago
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    @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...

  12. erin512
    • 3 years ago
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    @mathmate thank you so much :) so do you think 4 would be the correct answer in this case?

  13. mathmate
    • 3 years ago
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    Agree.

  14. erin512
    • 3 years ago
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    thank you so much :) i really appreciate it

  15. mathmate
    • 3 years ago
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    you're welcome! :)

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