Question

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???

Answer 1

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

Answer 2

are you allowed to substitued 1 into the other?

Answer 3

you can try

Answer 4

:/

Answer 5

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

Answer 6

yo.

Answer 7

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

Answer 8

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? :)

Answer 9

Wait what.

Answer 10

4?

Answer 11

this is another question.

Answer 12

get that junk into another question.

Answer 13

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

Answer 14

its not

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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?

Answer 19

nah, is good.

Answer 20

looking at too many problems at the same time.

Answer 21

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

Answer 22

Why is that?

Answer 23

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

Answer 24

I worked through the entire problem and got something different.

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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.

Answer 30

I think I already found my problem

Answer 31

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.

Answer 32

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

Answer 33

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.

Answer 34

Can you type out tour steps then, tim?

Answer 35

Alright.

Answer 36

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

Answer 37

Also, im NOT tim

Answer 38

then i subsituted into the other equation

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

-0.5y^2+30.5=0

Answer 43

y=sqrt(-30.5/-0.5)

Answer 44

y=7.81

Answer 45

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.

Answer 46

@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.

Answer 47

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

Answer 48

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

Answer 49

@NotTim

Answer 50

Wow, it deleted my wxplanatiom

Answer 51

Let me retype

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

You forgot to subtract 16.5^2 to both sides.

Answer 56

But the order is 3 I think.

Answer 57

wait wrong place what is that

Answer 58

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.

Answer 59

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

Answer 60

Unless you typed that wrong.

Answer 61

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

Answer 62

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

Answer 63

then -0.25y^4+272.25=-14

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

that's true.

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

Darnit i'm confused again.

Answer 72

Which step/part?

Answer 73

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

Answer 74

Correct

Answer 75

Alright, figured it out. Finally. Thanks mate.

Answer 76

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

Answer 77

Yeah, finally.

Answer 78

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

Answer 79

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

Answer 80

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