The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Simultaneous Equations with a Quadratic

I need to do this for my homework but I just can't figure it out, could someone guide me through please?

y=2x+1
y^2=8x
Original post by Isobel Sweeney
I need to do this for my homework but I just can't figure it out, could someone guide me through please?

y=2x+1
y^2=8x


You want to make an equation in terms of only x, or only y (you have to eliminate one of the variables). Can you think of how to do that?

Spoiler

Original post by Isobel Sweeney
I need to do this for my homework but I just can't figure it out, could someone guide me through please?

y=2x+1
y^2=8x


Rather than thinking of them as two separate equations, think of the first equation as being an identity for y. Because y is equal to 2x+1, we can use them interchangeably. Since we now know y in terms of x, it should be clear how we can get a quadratic in terms of x in the second equation, allowing us to solve for x.
Original post by StrangeBanana
You want to make an equation in terms of only x, or only y (you have to eliminate one of the variables). Can you think of how to do that?

Spoiler



thanks! Would that be x=y^2/8
and x=y-0.5?
Original post by Chlorophile
Rather than thinking of them as two separate equations, think of the first equation as being an identity for y. Because y is equal to 2x+1, we can use them interchangeably. Since we now know y in terms of x, it should be clear how we can get a quadratic in terms of x in the second equation, allowing us to solve for x.

thanks!
Original post by Isobel Sweeney
thanks! Would that be x=y^2/8
and x=y-0.5?


Not how I would have done it, but: your second equation is wrong. x = 0.5y - 0.5, not y - 0.5.
Original post by StrangeBanana
Not how I would have done it, but: your second equation is wrong. x = 0.5y - 0.5, not y - 0.5.


would it be better as (2x+1)^2=8x? or have i got this completely wrong?
Original post by Isobel Sweeney
would it be better as (2x+1)^2=8x? or have i got this completely wrong?


Yes, that'd be a better way to do it. :smile:
Original post by StrangeBanana
Yes, that'd be a better way to do it. :smile:

would i divide both sides by 8 then?
making (2x+1)^2/8=x? then i'm stuck again, do i have to set the quadratic to 0?
(thanks :smile:)
Original post by Isobel Sweeney
would i divide both sides by 8 then?
making (2x+1)^2/8=x? then i'm stuck again, do i have to set the quadratic to 0?
(thanks :smile:)


No, you'd multiply out the (2x+1)^2, and collect similar terms.
Reply 10
Avatar for Invest
Invest
14
First remove the y as you have above.

Then you get (2x+1)^2=8x

Before figuring out X, you have to get all the X's on one side.
(2x+1)(2x+1)=8x
Expand it.
4x^2+2x+2x+1=8x
4x^2+4x+2=8x
Now take 8x away from both sides so the right side is equal to 0.
4x^2+4x+2 -8x = 0
4x^2-4x+2=0
Now you could factorise.
(2x-1)(2x-1)=0
(2x-1)^2=0

If you know about factorising, you should know that one bracket must equal 0
so (2x-1) should equal 0.
What does X have to be for 2x-1 to equal 0?
2x=1
x=0.5

You're welcome.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you