cutiecomittee123
  • 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???
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
mathway.com quickmath.com i promise they help so much
NotTim
  • NotTim
are you allowed to substitued 1 into the other?
cutiecomittee123
  • cutiecomittee123
you can try

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

NotTim
  • NotTim
:/
NotTim
  • NotTim
you're suppose to try. i'm suppose to help.
NotTim
  • NotTim
yo.
NotTim
  • NotTim
why not re-arrange for x in the first equation, and sub it into the next equation.
anonymous
  • 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
  • NotTim
Wait what.
cutiecomittee123
  • cutiecomittee123
4?
NotTim
  • NotTim
this is another question.
NotTim
  • NotTim
get that junk into another question.
anonymous
  • anonymous
It would be 0. Are you sure 0 isnt one of the answer choices?
cutiecomittee123
  • cutiecomittee123
its not
anonymous
  • anonymous
Unless mobile is screwing with me that badly and the question i see is different than where Im typing :/
anonymous
  • anonymous
Although you dont have to be so rude about it either way -_-
NotTim
  • NotTim
ah. sorry, i'm working on 0 hrs of sleep, and university work and job applications. forgive me.
anonymous
  • 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
  • NotTim
nah, is good.
NotTim
  • NotTim
looking at too many problems at the same time.
anonymous
  • 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
  • NotTim
Why is that?
anonymous
  • 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
  • NotTim
I worked through the entire problem and got something different.
anonymous
  • anonymous
Well, do you see what i did to come across my solution?
NotTim
  • NotTim
Yeah, went to wolfram. It made sense. I'm double checking my answer now.
NotTim
  • 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
  • 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
  • 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
  • NotTim
I think I already found my problem
anonymous
  • 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
  • NotTim
I dunno. I worked thru it again, and I got 7.81=y.
anonymous
  • 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
  • anonymous
Can you type out tour steps then, tim?
NotTim
  • NotTim
Alright.
NotTim
  • NotTim
Rearranged x= (-y^2+33)/2
NotTim
  • NotTim
Also, im NOT tim
NotTim
  • NotTim
then i subsituted into the other equation
NotTim
  • NotTim
((-y^2+33)/2)^2+y^2+2((-y^2+33)/2)=19
NotTim
  • NotTim
(-0.5y^2+16.5)^2+y^2-y^2+33=19
NotTim
  • NotTim
-0.5y^2+y^2-y^2+16.5+33-19=0
NotTim
  • NotTim
-0.5y^2+30.5=0
NotTim
  • NotTim
y=sqrt(-30.5/-0.5)
NotTim
  • NotTim
y=7.81
NotTim
  • 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
  • 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
  • anonymous
Sorry, i kost wifi. Ill explain where in your steps you can get no solutiom nottim
anonymous
  • 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
  • anonymous
@NotTim
anonymous
  • anonymous
Wow, it deleted my wxplanatiom
anonymous
  • anonymous
Let me retype
anonymous
  • 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
  • anonymous
Well, it got deleted again. This time ill copy it in case that happens again, haha
anonymous
  • 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
  • NotTim
You forgot to subtract 16.5^2 to both sides.
NotTim
  • NotTim
But the order is 3 I think.
NotTim
  • NotTim
wait wrong place what is that
anonymous
  • 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
  • NotTim
(-0.5y^2+16.5)^2 = -14.
NotTim
  • NotTim
Unless you typed that wrong.
anonymous
  • anonymous
Thats after i cancelled y^2's and subtracted 33.
NotTim
  • NotTim
that would result in -0.25y^4+272.25= -14
NotTim
  • NotTim
then -0.25y^4+272.25=-14
anonymous
  • anonymous
No, it wouldnt. (-0.5y^2 +16.5)^2 = .25y^4 -16.5y^2 +272.25
NotTim
  • NotTim
why does 16.5^2 become -16.5y^2?
anonymous
  • 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
  • NotTim
that's true.
anonymous
  • anonymous
Bleh, sick of it deleting my messages. Stupid mobile, lol
NotTim
  • NotTim
Alright, you reasoning sounds perfect. Of course, I'm going to check once more, but everything you stated is sound.
anonymous
  • 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
  • NotTim
Darnit i'm confused again.
anonymous
  • anonymous
Which step/part?
NotTim
  • NotTim
(-0.5y^2+16.5)(-0.5y^2+16.5)+33= 19 was a step?
anonymous
  • anonymous
Correct
NotTim
  • NotTim
Alright, figured it out. Finally. Thanks mate.
anonymous
  • anonymous
Haha, okay. As long as everything makes sense. Do you come to no solution now?
NotTim
  • NotTim
Yeah, finally.
NotTim
  • NotTim
Same problem I had in high school. Didn't check over my work.
anonymous
  • anonymous
Lol, alright. Well, cutie closed the question, so not sure what conclusion she came to or if she made another question
anonymous
  • anonymous
Alright, sick of my wifi. Ill log back on once im in a position to set up my laptop. Laterz :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.