How many solutions are there to this system of equations?
2x+y^2=33
x^2+y^2+2x=19
1,2,3, or 4???

- cutiecomittee123

How many solutions are there to this system of equations?
2x+y^2=33
x^2+y^2+2x=19
1,2,3, or 4???

- Stacey Warren - Expert brainly.com

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- chestercat

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- anonymous

mathway.com
quickmath.com
i promise they help so much

- NotTim

are you allowed to substitued 1 into the other?

- cutiecomittee123

you can try

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## More answers

- NotTim

:/

- NotTim

you're suppose to try. i'm suppose to help.

- NotTim

yo.

- NotTim

why not re-arrange for x in the first equation, and sub it into the next equation.

- anonymous

Notice both equations have y^2 +2x in them. The first equation tells us this expression is equal to 33, so you can replace y^2 +2x for 33 in the second equation. Doing this gives
x^2 +33 = 19 or
x^2 = -14
How many solutions does that have? :)

- NotTim

Wait what.

- cutiecomittee123

4?

- NotTim

this is another question.

- NotTim

get that junk into another question.

- anonymous

It would be 0. Are you sure 0 isnt one of the answer choices?

- cutiecomittee123

its not

- anonymous

Unless mobile is screwing with me that badly and the question i see is different than where Im typing :/

- anonymous

Although you dont have to be so rude about it either way -_-

- NotTim

ah. sorry, i'm working on 0 hrs of sleep, and university work and job applications. forgive me.

- anonymous

Alright. So assuming mobile may be messing with me, i see the question as asking for how many solutions there are to the system
2x + y^2 = 33
X^2 + y^2 +2x = 19
Am i seeing the wrong question because of mobile?

- NotTim

nah, is good.

- NotTim

looking at too many problems at the same time.

- anonymous

Okay, then i stand by what i said. Her answer choices dont include 0 solutions. I can check wolfram to back me up, but might be slow on mobile, lol

- NotTim

Why is that?

- anonymous

Yeah, definitely 0 solutions. Cant copy the wolfram link on mobile. But what i did was perfectly fine and shows there is no solution

- NotTim

I worked through the entire problem and got something different.

- anonymous

Well, do you see what i did to come across my solution?

- NotTim

Yeah, went to wolfram. It made sense. I'm double checking my answer now.

- NotTim

http://www.wolframalpha.com/input/?i=2x%2By%5E2%3D33+and+x%5E2%2By%5E2%2B2x%3D19 is what you went thru right.

- anonymous

Yes, thats what i saw when i checked. Well, i can either try to better explain what i did or try and see where you had a mistake

- NotTim

Alright. I'm going to re-do my thing. If i do the same thing, I'll post it. If my results are in agreement, I'll tell ya. give me 3 minutes.

- NotTim

I think I already found my problem

- anonymous

Okay, thats good.
Either way, were trying to make a substitution that lets us reduce one of the equations to a single variable. Thankfully, we have a common y^2 + 2x in each equation. The first equation explicitly tells us that y^2 + 2x = 33. This will ways be true. Because the 2nd equation contains the same y^2 +2x, we can replace that chunk with 33.
x^2 +2x + y^2 = 19 becomes
x^2 + 33 = 19.
And then from there you can see the no solution result.

- NotTim

I dunno. I worked thru it again, and I got 7.81=y.

- anonymous

We could also show the same result by an elimination method, which is essentially going to be the same thing. Whichever way makes the result more visible to ya.

- anonymous

Can you type out tour steps then, tim?

- NotTim

Alright.

- NotTim

Rearranged x= (-y^2+33)/2

- NotTim

Also, im NOT tim

- NotTim

then i subsituted into the other equation

- NotTim

((-y^2+33)/2)^2+y^2+2((-y^2+33)/2)=19

- NotTim

(-0.5y^2+16.5)^2+y^2-y^2+33=19

- NotTim

-0.5y^2+y^2-y^2+16.5+33-19=0

- NotTim

-0.5y^2+30.5=0

- NotTim

y=sqrt(-30.5/-0.5)

- NotTim

y=7.81

- NotTim

Which doesn't make sense in the presence of wolfram alpha. I get that wolfram alpha sometimes get wrong data in context, but my written out answer doesn't collide well with that data.

- NotTim

@cutiecomittee123 In my conclusion, I believe it is 1. But don't trust me. both of us got different answers. But what you can take out of this conversation, is to rearrange 2x+y^2=33 into x=____ and then sub it into the other equation for x.

- anonymous

Sorry, i kost wifi. Ill explain where in your steps you can get no solutiom nottim

- anonymous

At the step youwhere you have (-0.5y^2 +16.5)^2 +y^2 -y^2 +33 = 19.
So let me cancel the y^2's and move the 33 to the other side. That would give
(-0.5y^2 +16.5)^2 = -14
Notice we have something squares equal to a negative value. This isnt possible and from here we can also conclude no solution

- anonymous

@NotTim

- anonymous

Wow, it deleted my wxplanatiom

- anonymous

Let me retype

- anonymous

So, the step where you have (-0.5y^2 +16.5)^2 +y^2 -y^2 +33 = 19.
Let me cancel the y^2's and move the 33 to the other side. This gives
(-0.5y^2 +16.5)^2 = -14.
Notice how we have a squared term equal to a negative value. From here we can see the no solution result
@NotTim

- anonymous

Well, it got deleted again. This time ill copy it in case that happens again, haha

- anonymous

At the step where you have (-0.y^2 + 16.5)^2 +y^2 - y^2 + 33 = 19
Ill cancel the y^2's and move the 33 to the other side. This gives
(-0.5y^2+16.5)^2 = -14.
Thus we have something squared equal to a negative value. This shows that we would have no solution since a value squared cannot equal something negative

- NotTim

You forgot to subtract 16.5^2 to both sides.

- NotTim

But the order is 3 I think.

- NotTim

wait wrong place what is that

- anonymous

Im just looking at your steps and i dont see where that would be. There wouldnt be a 16.5^2 to subtract. You have the entire quantity of (-0.5y^2 +16.5)^2, i cannot subtract 16.5^2 from here.

- NotTim

(-0.5y^2+16.5)^2 = -14.

- NotTim

Unless you typed that wrong.

- anonymous

Thats after i cancelled y^2's and subtracted 33.

- NotTim

that would result in -0.25y^4+272.25= -14

- NotTim

then -0.25y^4+272.25=-14

- anonymous

No, it wouldnt. (-0.5y^2 +16.5)^2 = .25y^4 -16.5y^2 +272.25

- NotTim

why does 16.5^2 become -16.5y^2?

- anonymous

Its a foiling problem if you were to expand it. That and squaring -0.5y^2 includes squaring the negative, it would disappear

- NotTim

that's true.

- anonymous

Bleh, sick of it deleting my messages. Stupid mobile, lol

- NotTim

Alright, you reasoning sounds perfect. Of course, I'm going to check once more, but everything you stated is sound.

- anonymous

But okay, lets write out each individual step of the foil
-0.5y^2 * -0.5y^2 = 0.25y^4
-0.5y^2 * 16.5 = -8.25y^2
16.5 * -0.5y^2 = -8.25y^2
16.5 * 16.5 = 272.25
put it together and you have
0.25y^4 -16.5y^2 + 272.25

- NotTim

Darnit i'm confused again.

- anonymous

Which step/part?

- NotTim

(-0.5y^2+16.5)(-0.5y^2+16.5)+33= 19 was a step?

- anonymous

Correct

- NotTim

Alright, figured it out. Finally. Thanks mate.

- anonymous

Haha, okay. As long as everything makes sense. Do you come to no solution now?

- NotTim

Yeah, finally.

- NotTim

Same problem I had in high school. Didn't check over my work.

- anonymous

Lol, alright. Well, cutie closed the question, so not sure what conclusion she came to or if she made another question

- anonymous

Alright, sick of my wifi. Ill log back on once im in a position to set up my laptop. Laterz :)

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