Find the intersection points, if any, for each system of equations:
(photo attached)

Question

Find the intersection points, if any, for each system of equations: 
(photo attached)

anonymous · Answer

attachment

anonymous · Answer

Looks gnarly. 

can you try solving for y in the first equation?

anonymous · Answer

how?

anonymous · Answer

Get everything besides y on the right side,  subtract x^2 and 39 first

anonymous · Answer

don't really how  to do that because there are 2 y's

anonymous · Answer

Avoid roots and stuff by solving for x instead. $$x ^{2}=y ^{2}-9$$It will skip some headaches.

anonymous · Answer

thanks :)

anonymous · Answer

... and that was from the second eqn.

anonymous · Answer

Then sub into first equation and reduce.

anonymous · Answer

what would that be if i plugged it in @EulerGroupie

anonymous · Answer

I get
$$(y ^{2}-9)+y ^{2}-16y+39=0$$

anonymous · Answer

oh okay i see

anonymous · Answer

Solve it as a quadratic in one variable... (factor, quadratic formula, or complete the square)

anonymous · Answer

how is that done? sorry for all the questions

anonymous · Answer

Can you simplify the eqn I gave you (2 like terms...)?

anonymous · Answer

i got y=3,5

anonymous · Answer

Nice... that was the hard part.

anonymous · Answer

what comes after that?

anonymous · Answer

put y back into one of the equations... first as 3... then as 5.

anonymous · Answer

I picked the simpler of the two (and the one we simplified)
$$x ^{2}=y ^{2}-9$$
first
$$x ^{2}=3^{2}-9$$x=0

anonymous · Answer

Now try 5 in there and you'll get two answers when y=5.

anonymous · Answer

so in that case what would the final answer be?

anonymous · Answer

tsk, tsk... you tell me

anonymous · Answer

ahh i dont know

anonymous · Answer

$$x ^{2}=y ^{2}-9$$y=5$$x ^{2}=5^{2}-9$$

anonymous · Answer

ok what comes after that

anonymous · Answer

square 5... subtract 9... square root both sides (don't forget plus or minus)

anonymous · Answer

would that be 4?

anonymous · Answer

one of them... when you square root both sides, you must consider plus AND minus.

anonymous · Answer

what would the other side be

anonymous · Answer

-4

anonymous · Answer

oh okay, so how would that fit into the final answer

anonymous · Answer

So I get three points: (4,5), (-4,5), (0,3)
If you graphed both of these equations... the top one is a circle of radius 5 centered at (0,8) and the bottom is a hyperbola centered at the origin opening up and down with vertices at +/-3.

anonymous · Answer

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