Question

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

Answer 1

the choices are 1,2,3, and 4

Answer 2

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

Answer 3

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

Answer 4

i will figure it out afterwards, i just need an answer quickly, please help

Answer 5

thank you :)

Answer 6

Hint:

Answer 7

@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

Answer 8

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 :(

Answer 9

@amstro

Answer 10

@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...

Answer 11

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

Answer 12

Agree.

Answer 13

thank you so much :) i really appreciate it

Answer 14

you're welcome! :)