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Simtaneous equation help

I am so confused and stuck on this question:

1.

Solve the simultaneous equations xy=2 and 3y-2x=11

How would I go about solving this? Could you give me my first step?


Original post by socialgain
I am so confused and stuck on this question:

1.

Solve the simultaneous equations xy=2 and 3y-2x=11

How would I go about solving this? Could you give me my first step?




When you have non-linear it is usually a good idea to use substitution
For this you want to isolate one of the variables

In this example, I would start with 3y = 11 + 2x

I would then substitute that into 3xy = 6
The first step would be to rearrange one of the equations to leave either x or y on one side by itself.
Original post by socialgain
I am so confused and stuck on this question:

1.

Solve the simultaneous equationsxy=2and3y-2x=11

How would I go about solving this? Could you give me my first step?




Xy = 2 and 3y-2x =11

Rearrange one of dem equations, i'll do da one one the left innit:
X = 2/y

Now sub dat into da other equation and u can solve da equation innit

Easy, fam

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Reply 4
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socialgain
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2
Original post by QuantumSuicide
Xy = 2 and 3y-2x =11

Rearrange one of dem equations, i'll do da one one the left innit:
X = 2/y

Now sub dat into da other equation and u can solve da equation innit

Easy, fam

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X=2/y
3y-2x=11
3y-2(2/y)=11
3y-4/y=11
3y2-4=11y
y=(3y2-4)/11

What now? Have I done it right? Still confused -_-
Original post by socialgain
X=2/y
3y-2x=11
3y-2(2/y)=11
3y-4/y=11
3y2-4=11y
y=(3y2-4)/11

What now? Have I done it right? Still confused -_-


Do not do that last line

You had a quadratic in the previous line
Reply 6
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socialgain
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Original post by TenOfThem
When you have non-linear it is usually a good idea to use substitution
For this you want to isolate one of the variables

In this example, I would start with 3y = 11 + 2x

I would then substitute that into 3xy = 6


Right so 3xy = 6
3x(11+2x) = 6
3x(33+6x) = 6
99x+18x2=6
x(99+18x) = 6
x=6/99+18x
Reply 7
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socialgain
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Original post by TenOfThem
Do not do that last line

You had a quadratic in the previous line


OH right yeah
3y2-4=11y
3y2-11y-4 = 0
Then I just have to solve it?
Original post by socialgain
Right so 3xy = 6
3x(11+2x) = 6
3x(33+6x) = 6
99x+18x2=6
x(99+18x) = 6
x=6/99+18x


edit

you seem to have multiplied by 3 - where did 33+6x come from?
Original post by socialgain
OH right yeah
3y2-4=11y
3y2-11y-4 = 0
Then I just have to solve it?


yes
Reply 10
Avatar for davros
davros
16
Original post by socialgain
X=2/y
3y-2x=11
3y-2(2/y)=11
3y-4/y=11
3y2-4=11y
y=(3y2-4)/11

What now? Have I done it right? Still confused -_-


When you get to this point:

3y2-4=11y

I would suggest rearranging into the standard form of a quadratic equation and trying to factorize.
Reply 11
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socialgain
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Original post by TenOfThem
yes


3y2-11y-4 = 0
So using the quadratic formula the answers would be
-0.3, 4
is that the final answer?
Original post by socialgain
3y2-11y-4 = 0
So using the quadratic formula the answers would be
-0.3, 4
is that the final answer?


Those are the answers for y - you need the answers for x as well
Reply 13
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socialgain
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Original post by TenOfThem
Those are the answers for y - you need the answers for x as well


so xy=2
x=2/y
x=2/-0.3 = -6.6

x=2/4 = 0.5

y=-0.3, y=4
x=-6.6, x=0.5

is this correct?
Original post by socialgain
so xy=2
x=2/y
x=2/-0.3 = -6.6

x=2/4 = 0.5

y=-0.3, y=4
x=-6.6, x=0.5

is this correct?


You need to give your answers in pairs and fractions would be better than decimals

By pairs I mean putting the connected x and y as an answer
Reply 15
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socialgain
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Original post by TenOfThem
You need to give your answers in pairs and fractions would be better than decimals

By pairs I mean putting the connected x and y as an answer


So y=-0.3, x = -6.6
y=4, x = 1/2

Is this correct?
Original post by socialgain
So y=-0.3, x = -6.6
y=4, x = 1/2

Is this correct?

yes
Original post by socialgain
So y=-0.3, x = -6.6
y=4, x = 1/2

Is this correct?


Well done, my friend. I have taught you well

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Reply 18
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socialgain
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Original post by QuantumSuicide
Well done, my friend. I have taught you well

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Haha thanks, and you too ten

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