Solve the following system of equations.
x^2 + y^2 = 9
x^2 - 3y = 9

Question

Solve the following system of equations. 
x^2 + y^2 = 9 
x^2 - 3y = 9

beccab003 · Answer

These are the options:
(-3, 0), (3, 0),(-3, 9),(3, 9) 
(-3, 9),(-3, 0) 
(-3, 0), (0, -3), (3, 0) 
(-3, 9)

I am very confused on how to do this problem because there is a 3y and y^2

anonymous · Answer

well since they both = 9 its safe to say they equal each other right @BeccaB003

anonymous · Answer

hello

anonymous · Answer

well since they both = 9 its safe to say they equal each other right @BeccaB003

beccab003 · Answer

I am here. Yes, I suppose they would equal each other.

welshfella · Answer

x^2 + y^2 = x^2 - 3y

anonymous · Answer

so x^2 + y^2 = x^2 - 3y
now solve do -x^2 to get
y^2+-3y

anonymous · Answer

i mean y^2=-3y

welshfella · Answer

subtract x^2 from both sides
y^2 = - 3y

beccab003 · Answer

@welshfella @DaBest21  But how do you solve with that problem if there is y and y^2?

welshfella · Answer

can you solve that?

beccab003 · Answer

I thought you used substitution or elimination for problems like this.

beccab003 · Answer

I don't understand how you would solve for y^2=3y ---they are two different types of variables. you can't combine them or anything.

welshfella · Answer

well i have used elimination  - i eliminated x^2

welshfella · Answer

y^2 + 3y = 0
y(y + 3) = 0

y = ?

welshfella · Answer

you factor them as above

beccab003 · Answer

y(y+3)=0 <---------- is factored

beccab003 · Answer

I don't know how to simplify that more.

welshfella · Answer

when  2 functions are multiplied together and the result is 0 then either one  or the other is zero. I other words there are 2 solutions

y(y + 3) = 0

y = 0 or y + 3 = 0
y = 0  y= -3

0 and -3 are the 2 solutions

beccab003 · Answer

So then you plug them both into the original equation to find x?

welshfella · Answer

yes plug them into 
x^2 - 3y = 9

welshfella · Answer

so when y = -3
x^2 -3(-3) = 9
x^2 + 9 = 9
x^2 = 9-9 = 0
x = 0

so one solution is (0,-3)

beccab003 · Answer

Okay so, x^2 -3(0) = 9
equals: x^2 = 9 
= x = 3

beccab003 · Answer

So another solution is (3,0)

welshfella · Answer

not quite  sqrt x^2  is also -3

welshfella · Answer

right (3,0) is one solution and a third one is (-3,0)

welshfella · Answer

* square root of 9 is also -3

beccab003 · Answer

How can the square root of 9 be -3?

welshfella · Answer

so the 3rd option is the correct one.

anonymous · Answer

c

welshfella · Answer

3 * 3 = 9
also 
-3 * -3 = 9

beccab003 · Answer

Okay, Thank you so much for your help! :)

welshfella · Answer

yw