## erin512 2 years ago What is the maximum number of possible solutions for the system shown below?

1. erin512

2. erin512

the choices are 1,2,3, and 4

3. amstro

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

what would the final answer be in that case? @amstro

5. erin512

6. erin512

thank you :)

7. mathmate

Hint: |dw:1358003669486:dw|

8. amstro

@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

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

@amstro

11. mathmate

@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

@mathmate thank you so much :) so do you think 4 would be the correct answer in this case?

13. mathmate

Agree.

14. erin512

thank you so much :) i really appreciate it

15. mathmate

you're welcome! :)