simultaneous equation

[ana_mujahid]

y=3x-1
x(sq) + y (sq) = 5

is the answer 2 and 1?

please show ur steps

[ana_mujahid]

any1:(

[Rosalie-Beauty]

any1:(

ARRG! I thought I escaped math when I left school. Now its sent agents after me for torture

ignore me, I am being overly dramatic.

[Ibn Al-Jarrah]

theres 3 ways of doing this

Elimination - where you take one equation from the other so you are left with only one x or y

Subsititution - where you make x= sumin in terms of y and then substitute it into the equation

and a third 1:scratch:

anyway substitution method:

y=3x-1 (eqn 1)

but we also know y^2 (squared) + x^2 = 5 (eqn 2)

therefore (3x-1)^2 + x^2 = 5
9x^2 - 6x +1 +x^2 = 5

therefore 10x^2 - 6x + 1=5 bring the 5 over:

10x^2 -6x -4=0 factorise:

:scratch: its either (10x...)(x...) or (5x...)(2x...)

this is long. mayb the other way was better. Thing is if you used elimination you would need to root eqn 2 which makes it much harder.

basically u solve that, find out what x is and then use that to find out y:up:

[Ibn Al-Jarrah]

its definitely (5x...)(2x...)

just need to find out the rest

[ana_mujahid]

theres 3 ways of doing this

Elimination - where you take one equation from the other so you are left with only one x or y

Subsititution - where you make x= sumin in terms of y and then substitute it into the equation

and a third 1:scratch:

anyway substitution method:

y=3x-1 (eqn 1)

but we also know y^2 (squared) + x^2 = 5 (eqn 2)

therefore (3x-1)^2 + x^2 = 5
9x^2 - 6x +1 +x^2 = 5

therefore 10x^2 - 6x + 1=5 bring the 5 over:

10x^2 -6x -4=0 factorise:

:scratch: its either (10x...)(x...) or (5x...)(2x...)

this is long. mayb the other way was better. Thing is if you used elimination you would need to root eqn 2 which makes it much harder.

basically u solve that, find out what x is and then use that to find out y:up:

so ur saying there is more than one answer?

ARRG! I thought I escaped math when I left school. Now its sent agents after me for torture

ignore me, I am being overly dramatic.

:up: welcome back to mathematics :D were nothing could go wrong!

except if u mix up pythagoras with trigonomentry like i done in my exam :mad:

[Ibn Al-Jarrah]

so ur saying there is more than one answer?


since theres a squared, it means you have two roots which could mean more than one answer. think of it like graphs (HEY thats the 3rd method) its one straight like and a curve (circle to be precise). the line could go through the curve twice which mans theres 2 answers, or it could just touch it once.

i think the factorisation is (5x+3)(2x-2)

edit: its not, that gives 10x^2 -4x -6 :(

[Ibn Al-Jarrah]

Alhamdulillah!

its (10x +4)(x-1)=0

since they multiply together to make 0, one of them has to be 0.

therefore either 10x+4=0 (in which case x=-4/10) or x-1=0 in which case x=1

now we use these two to find out y using eqn 1:

y=3x-1

(if x=1), y is 3-1=2
if x = -4/10, y is (-12/10) - 1 = -2/10

in short: x=1, y=2
x=-4/10, y=-2/10
now to check it you use the second formula.

x^2 + y^2 = 5

using first solutions: 1^2 + 2^2 is 1+4=5 Alhamdulillah
using second solutions (-4/10)^2 + (-2/10) =...(this could get nasty)...0.16 + 0.04 which is no where near 10

therefore there is only one set of solutions: x=1, y=2


am i good or what

[ana_mujahid]

since theres a squared, it means you have two roots which could mean more than one answer. think of it like graphs (HEY thats the 3rd method) its one straight like and a curve (circle to be precise). the line could go through the curve twice which mans theres 2 answers, or it could just touch it once.

i think the factorisation is (5x+3)(2x-2)

edit: its not, that gives 10x^2 -4x -6 :(

so could the answer be 2 and 1 :( cuz thats what i wrote on my exam today
which reminds me i need to be revising for 2mro :(

[Rosalie-Beauty]

:up: welcome back to mathematics :D were nothing could go wrong!

except if u mix up pythagoras with trigonomentry like i done in my exam :mad:

Ahh! *developing headache* Math is utterly boring, no stories, pictures, no people, just mindless numbers.

but I guess I should not be saying this to a bunch of math geeks. :o

[Ibn Al-Jarrah]

so could the answer be 2 and 1 :( cuz thats what i wrote on my exam today
which reminds me i need to be revising for 2mro :(

The third method is basically draw a graph of the 2 equations and see where they meet. If you did it for these equations, they would meet at (1,2)


Ahh! *developing headache* Math is utterly boring, no stories, pictures, no people, just mindless numbers.

but I guess I should not be saying this to a bunch of math geeks.

hey, algebra was an islamic invention:nerdbro: u never know when you need differentiation in life:rolleyes:

[ana_mujahid]

Ahh! *developing headache* Math is utterly boring, no stories, pictures, no people, just mindless numbers.

but I guess I should not be saying this to a bunch of math geeks. :o

maths is simple 1+1 = 2
english lit is confussing, all poems, read behind the lines, so unusual, no straight forward answers
:zzz::zzz::zzz::zzz::zzz::zzz:

lol no offence but if i take lit in a-lvls and uni, ill be the worlds biggest english lit flop!:hidban:

:inlove::inlove:maths and science:inlove::inlove:

[ana_mujahid]

The third method is basically draw a graph of the 2 equations and see where they meet. If you did it for these equations, they would meet at (1,2)




hey, algebra was an islamic invention:nerdbro: u never know when you need differentiation in life:rolleyes:

ahha i see
well i hope i get it correct cuz it a 6 mark question


yep algebra come from Al-Jubayr (or a similar name), i think he came from babylon (iraq atm)

duno

[Rosalie-Beauty]

The third method is basically draw a graph of the 2 equations and see where they meet. If you did it for these equations, they would meet at (1,2)




hey, algebra was an islamic invention:nerdbro: u never know when you need differentiation in life:rolleyes:

I dont plan on it. Poetry was also prominent in Islam. The Quran itself is poetry, the verses rhyme and flow. That's something math cant ever do, it cant sound beautiful.

[Ibn Al-Jarrah]

I dont plan on it. Poetry was also prominent in Islam. The Quran itself is poetry, the verses rhyme and flow. That's something math cant ever do, it cant sound beautiful.

:rubeyes::torture:


Poetry's nice, but maths is used in the REAL world.


LOL also, have you ever read Carol Anne Duffy?:eek:

[Rosalie-Beauty]

:rubeyes::torture:


Poetry's nice, but maths is used in the REAL world.


LOL also, have you ever read Carol Anne Duffy?:eek:

True math is used in the real world, but Writers are the famous ones. I have never heard the announcer say, "..and now presenting..the world famous mathmetician!" lol. Imagination is the apex of intelligence.

No I have never read that. Never even heard of it.

[ana_mujahid]

:rubeyes::torture:


Poetry's nice, but maths is used in the REAL world.


LOL also, have you ever read Carol Anne Duffy?:eek:

ive not only read her poems, we had to go on a trip to see her and other poets, no offence, BUT IT WAS BOOOOOOOOOOOOOOOOOOOORING! except the last guy, his poem was jokes :rolleyes: londoner londoner londoner.....:rolleyes: weird yet funny :D

[Ibn Al-Jarrah]

MAAN by the end of my GCSEs i ws gna kill her:torture: her poems dont even rhyme!!

Stealing by Carol anne duffy

The most unusual thing I ever stole? A snowman.
Midnight. He looked magnificent; a tall, white mute
beneath the winter moon. I wanted him, a mate
with a mind as cold as the slice of ice
within my own brain. I started with the head.

Better off dead than giving in, not taking
what you want. He weighed a ton; his torso,
frozen stiff, hugged to my chest, a fierce chill
piercing my gut. Part of the thrill was knowing
that children would cry in the morning. Life's tough.

Sometimes I steal things I don't need. I joy-ride cars
to nowhere, break into houses just to have a look.
I'm a mucky ghost, leave a mess, maybe pinch a camera.
I watch my gloved hand twisting the doorknob.
A stranger's bedroom. Mirrors. I sigh like this - Aah.

It took some time. Reassembled in the yard,
he didn't look the same. I took a run
and booted him. Again. Again. My breath ripped out
in rags. It seems daft now. Then I was standing
alone among lumps of snow, sick of the world.

Boredom. Mostly I'm so bored I could eat myself.
One time, I stole a guitar and thought I might
learn to play. I nicked a bust of Shakespeare once,
flogged it, but the snowman was the strangest.
You don't understand a word I'm saying, do you?

NO!!! i dont!

[ana_mujahid]

MAAN by the end of my GCSEs i ws gna kill her:torture: her poems dont even rhyme!!

Stealing by Carol anne duffy



NO!!! i dont!

nor did i :|

[ana_mujahid]

answer to my question:

1) y = 3x - 1

2) x^2 + y^2 = 5

x^2 + (3x - 1)^2 = 5

x^2 + 9x^2 - 6x + 1 = 5

10x^2 - 6x - 4 = 0

5x^2 - 3x - 2 = 0

5x^2 - 5x + 2x - 2 = 0 {rewrite for grouping}

(5x + 2)(x - 1) = 0

x = -2, 1

When x = -2, y = -7

When x = 1, y = 2

[Ibn Al-Jarrah]

True math is used in the real world, but Writers are the famous ones. I have never heard the announcer say, "..and now presenting..the world famous mathmetician!" lol. Imagination is the apex of intelligence.

No I have never read that. Never even heard of it.

Thats the thing - poets are usually self obsessed weirdos, with no other way of making money. Mathematicians work discreetly and don't need fame. Its like them arty farty people who buy useless pieces of 'art' for millions. Im not generalising, but theres a lot of rubbish out there.

[Ibn Al-Jarrah]

answer to my question:

1) y = 3x - 1

2) x^2 + y^2 = 5

x^2 + (3x - 1)^2 = 5

x^2 + 9x^2 - 6x + 1 = 5

10x^2 - 6x - 4 = 0

5x^2 - 3x - 2 = 0

5x^2 - 5x + 2x - 2 = 0 {rewrite for grouping}

(5x + 2)(x - 1) = 0

x = -2, 1

When x = -2, y = -7

When x = 1, y = 2

i dont think you can divide by 2 can you? Then again, you are doing it to both sides, and you got the answer.

[Rosalie-Beauty]

Thats the thing - poets are usually self obsessed weirdos, with no other way of making money. Mathematicians work discreetly and don't need fame. Its like them arty farty people who buy useless pieces of 'art' for millions. Im not generalising, but theres a lot of rubbish out there.

I do agree with the utter sillyness buying useless things, but not all writers are self-obsessed. Some of them only get famous after they die. And think about it, when a person puts his/her ideas on paper they live there forever, even after they are long gone, they live on in there books, lending advice to generations after. True some of them may not have a steady job, but whay does it matter? There happy, and the few people who's hearts the did touch was worth their while.

[Ibn Al-Jarrah]

I do agree with the utter sillyness buying useless things, but not all writers are self-obsessed. Some of them only get famous after they die. And think about it, when a person puts his/her ideas on paper they live there forever, even after they are long gone, they live on in there books, lending advice to generations after. True some of them may not have a steady job, but whay does it matter? There happy, and the few people who's hearts the did touch was worth their while.

aww isnt that nice...(EDIT) well maths lives forever as well. True, you can't exactly use it in everyday life but we use it more than we know. Thing is poetry can be corrupted - the Makkans during Jahiliyyah used poetry as propanganda against Muhammad SAWS.

There are some good poems though. I liked this one from the anthology -

Eagle
He clasps the crag with crooked hands;
Close to the sun in lonely lands,
Ring'd with the azure world, he stands.

The wrinkled sea beneath him crawls;
He watches from his mountain walls,
And like a thunderbolt he falls.

-- Alfred, Lord Tennyson

shame we didnt study it

[Rosalie-Beauty]

aww isnt that nice...:torture: well maths lives forever as well. True, you can't exactly use it in everyday life but we use it more than we know. Thing is poetry can be corrupted - the Makkans during Jahiliyyah used poetry as propanganda against Muhammad SAWS.

There are some good poems though. I liked this one from the anthology -

Eagle
He clasps the crag with crooked hands;
Close to the sun in lonely lands,
Ring'd with the azure world, he stands.

The wrinkled sea beneath him crawls;
He watches from his mountain walls,
And like a thunderbolt he falls.

-- Alfred, Lord Tennyson

shame we didnt study it


Whats with the :torture:

[ana_mujahid]

fight fight :D

[Rosalie-Beauty]

fight fight :D

sad, utterly sad.

[ana_mujahid]

sad, utterly sad.

the revision got to me, ive become crazy :D

lol

nways, me seriously need to revise for RE now, its 9:20 already and ive not even started

btw i got a english lit exam next week, u can help me with that :p :up: if u dnt mind,

remember me in ur dua's insha'ALLAH and ill remember u,
u2 akhi Ibn Al-Jarrah

:jkk:

:wswrwb:

[Kubs]

Do you understand the question now or would you like me to write down the answer? :)

[ana_mujahid]

Do you understand the question now or would you like me to write down the answer? :)

i understood the question, no need to post further answers, :jkk: anyway :)

[Metroid]

answer to my question:

1) y = 3x - 1

2) x^2 + y^2 = 5



I did not know you meant "X²" by "sq" and i assumed that "sp" was another variable. :torture:

Even with my wrong assumption, I was able to solve it:torture:


Now, I want you to solve this your own equation considering that:
sp is a single variable which mean you replace by the letter A for ease. in other words solve
1) y=3X+1
2) X*A+X*A=5

:torture:

[ahimjin]

Well the other method of solving these equations are by the use of Matrices. Either use the Inverse method or Crammers rule or the Gaussian elimination. I use the crammers rule a lot if I have a system of three equations

[zahra_unknown]

answer to my question:

1) y = 3x - 1

2) x^2 + y^2 = 5

x^2 + (3x - 1)^2 = 5

x^2 + 9x^2 - 6x + 1 = 5

10x^2 - 6x - 4 = 0

5x^2 - 3x - 2 = 0

5x^2 - 5x + 2x - 2 = 0 {rewrite for grouping}

(5x + 2)(x - 1) = 0

x = -2, 1

When x = -2, y = -7

When x = 1, y = 2

i get x = -2/5 or x = 1 ?? :rubeyes:

Why?

[ana_mujahid]

i get x = -2/5 or x = 1 ?? :rubeyes:

Why?

u might have a wrong calculation

post ur calculations and insha'ALLAH we'll find the problem;)

[zahra_unknown]

Most of it is the same..



y = 3x - 1
x^2 + y^2 = 5
So.. Subtitute equation 1 into equation 2 and you get..

x^2 + (3x - 1)^2 = 5

x^2 + 9x^2 - 6x + 1 = 5

10x^2 - 6x - 4 = 0

5x^2 - 3x - 2 = 0

5x^2 - 5x + 2x - 2 = 0

Therefore

5x(x - 1) + 2 (x - 1) = 0

(5x + 2) (x - 1) = 0

And so either
5x = -2
Which means x = -2 /5

Or x = 1