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Simultaneous equations GCSE

iPad User

Y= 11X + 3
Y= 4x^2

Please walk me through step by step, I will positive rate your profile :smile:

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Reply 1

username360639

you have to link them together so 11x+3=4x^2...rearrange giving 4x^2-11x-3...times -3 and 4 together giving -12, then solve the quadratic....4x^2-11x-12, two numbers that add to give -11 and times to give -12....so that will be 4x^2+1x-12x-3....factorise them -giving 4x(x-3)+1(x-3)..so your final answer should be (4x+1) and (x-3)...x=3 and x=-1/4, sub into any y equations giving y=11(3)+3, y=36 and y=11(-1/4)+3 giving your other answer ...thats how i think you should do it..anyone want to clarify my answer it might be wrong :s-smilie:

(edited 12 years ago)

Reply 2

gozatron

Original post by iPad User

Y= 11X + 3
Y= 4x^2

Please walk me through step by step, I will positive rate your profile :smile:

Have you heard of solving by substitution?

Reply 3

Kimiechi

Rearrange the first one to give : 3 = y - 11x
Substitute in the second one : 4x^2 - 11x = 3
Rearrange to get a quadratic equation : 4x^2 - 11x - 3 = 0
Factorize the quadratic : 4x^2 -12x + 1x - 3
4x(x-3) / -1(x-3)
(4x -1)(x-3)
Then solve normally: x = 1/4 or x = 3

Reply 4

Kimiechi

Oops I forgot the y bit but it'll be the same as ,,,, above

Reply 5

proud nd luvin it

Right, you put theme equal to each other:
11x+3=4x^2
Rearrange:
4x^2-11x-3=0
Factorise into 2 brackets:
(4x+1)(x-3)=0
Then split it up:
4x+1=0
x-3=0

and work out x :smile:

and sub it back into the y equation

(edited 12 years ago)

Reply 6

proud nd luvin it

Original post by ,,,,

you have to link them together so 11x+3=4x^2...rearrange giving 4x^2-11x-3...times -3 and 4 together giving -12, then solve the quadratic....4x^2-11x-12, two numbers that add to give -11 and times to give -12....so that will be 4x^2+1x-12x-3....factorise them -giving 4x(x-3)+1(x-3)..so your final answer should be (4x+1) and (x-3)...x=3 and x=-1/4, sub into any y equations giving y=11(3)+3, y=33 and y=11(-1/4)+3 giving your other answer ...thats how i think you should do it..anyone want to clarify my answer it might be wrong :s-smilie:

Why one earth would you do that? :lolwut:

do what?

Original post by ,,,,

do what?

times the -3 and 4 together bit

Reply 9

username360639

you negged me didnt you LOL....urm well that's how i was taught?

Reply 10

Stormwhite

Just sub one of the values into the other, you get

4x^2-11x-3=0

This is a quadratic equation, you can use the quadratic formula or factorise it

(4x+1)(x-3)

Giving the answers

x=-1/4[br]x=3

Sub those in to the linear equation to find the corresponding y values.

Reply 11

iPad User

Original post by Stormwhite

Just sub one of the values into the other, you get

4x^2-11x-3=0

This is a quadratic equation, you can use the quadratic formula or factorise it

(4x+1)(x-3)

Giving the answers

x=-1/4[br]x=3

Sub those in to the linear equation to find the corresponding y values.

The Y bit is what I'm stuck on... lol

Reply 12

proud nd luvin it

Original post by ,,,,

you negged me didnt you LOL....urm well that's how i was taught?

lmao no I didn't! :') I have repped too many people today already :tongue:

Oh, ok, it just seemed a strange way to do it!

Reply 13

proud nd luvin it

Original post by iPad User

The Y bit is what I'm stuck on... lol

Well just use your x values, and sub them into the original equation, to work out y...?

Reply 14

username360639

LOOL ahh never mind then...i guess theres more than one way of doing things :smile:

Reply 15

username360639

Original post by proud nd luvin it

Well just use your x values, and sub them into the original equation, to work out y...?

LOL...come on ipad user its not that hard! use 3 and -1/4 in one of the above equations

Reply 16

Dizzy in my Head

Original post by iPad User

Y= 11X + 3
Y= 4x^2

Please walk me through step by step, I will positive rate your profile :smile:

Ok, well. There is one linear equation in there (doesn't have a power to the X). So you substitute the Y = 11X + 3 into the other equation Y= 4x^2.

This would become 4x^2 = 11X + 3.

You would rearrange it to get it all to one side of the quation and it would become 4x^2 - 11X - 3 = 0.

You would then factorise (you know how to do this, right?)

(4X + 1) (X - 3) = 0

And to make each bracket equal zero (you have to get X as the subject of the equation):

4X + 1 = 0
4X = -1
Therefore X = -1/4

and:

X - 3 = 0
X = 3

Substitute both values into the equation (the linear is easiest to do), so:

Y = 11X + 3

For X = -1/4, Y = 11(-1/4) + 3 = 1/4

For X = 3, Y = 11(3) + 3 = 36

So the answer is X = -1/4 and Y = 1/4, and X = 3 and Y = 36

Haven't done them in ages, so please correct me if I'm wrong! :wink:

Please quote me if you want anything explaining that didn't make sense. I have some useful websites you can look at if you still don't get it. :smile:

(edited 12 years ago)

Reply 17

username360639