simultaneous equations Watch

hangulmaster
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Hi

I have been trying to understand this simultaneous equations for along time but I just dont understand i dont understand any of the material online at all.

the question

y-2x=17
x-y=-8
im confused because when solving for x the number doesn't divide into 17at all so what am i supposed to do? in addition i get really confused when finding the y value as well?

can someone please explain fully and in simple terms how you solve this type of equation?
thank you
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Den987
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So you have:

y - 2x = 17
x - y = -8

You firstly rearrange the equation to equal x (you can do y too, but in this case it is simpler).
So x = -8 + y

Now you substitute in the other equation to solve for y
y - 2( -8 + y) = 17
y - 2(y - 8) = 17
y - 2y + 16 = 17
-y + 16 = 17
-y = 1
y = -1

Now you add this value to solve for x
x - (-1) = -8
x + 1 = -8
x = - 9

Therefore
x = -9
y = -1

And you can double check by adding these values to the original equations

So (-1) - 2(-9)
- 1 + 18 = 17

And (-9) - ( - 1)
- 9 + 1 = -8

So both values are correct

Hope this helps

(Original post by hangulmaster)
Hi

I have been trying to understand this simultaneous equations for along time but I just dont understand i dont understand any of the material online at all.

the question

y-2x=17
x-y=-8
im confused because when solving for x the number doesn't divide into 17at all so what am i supposed to do? in addition i get really confused when finding the y value as well?

can someone please explain fully and in simple terms how you solve this type of equation?
thank you
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sunshinehss
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Lmao I solved this as well because this was my favourite thing at GCSE aka the one thing I knew I was sure to get marks on 😭😭 wanted to see if i still had it (👀 very questionable 😂)

Anyhoo I'll upload my working out in a bit
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hangulmaster
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like how do you do that my brain ...my confusion
(Original post by Den987)
So you have:

y - 2x = 17
x - y = -8

You firstly rearrange the equation to equal x (you can do y too, but in this case it is simpler).
So x = -8 + y

Now you substitute in the other equation to solve for y
y - 2( -8 + y) = 17
y - 2(y - 8) = 17
y - 2y + 16 = 17
-y + 16 = 17
-y = 1
y = -1

Now you add this value to solve for x
x - (-1) = -8
x + 1 = -8
x = - 9

Therefore
x = -9
y = -1

And you can double check by adding these values to the original equations

So (-1) - 2(-9)
- 1 + 18 = 17

And (-9) - ( - 1)
- 9 + 1 = -8

So both values are correct

Hope this helps
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mqb2766
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Are you trying to solve it by substitution or by elimination?
They're similar, but if you're not sure about what they are, have a read of your notes first.
(Original post by hangulmaster)
like how do you do that my brain ...my confusion
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hangulmaster
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which one of those is most appropriate for which type of simultaneous equation question like i mean can you apply both of those methods to any simultaneous equation and it work just as well? you know what i mean? , because the different variations of questions its hard to apply sometimes to my question if its different etc
i dont know if that made sense like its hard because in the question i gave numbers didn't divide properly into each other which is really confusing ?
honestly been trying understand simultaneous equations for at least 2 years at this point . i think its a hopeless situation at this point
(Original post by mqb2766)
Are you trying to solve it by substitution or by elimination?
They're similar, but if you're not sure about what they are, have a read of your notes first.
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mqb2766
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Which notes are you looking at?
Does
https://www.bbc.com/bitesize/guides/z9y9jty/revision/1
make any sense?

If so, Ill guide you through solving it using both methods. It should not take you 2 years to understand.

(Original post by hangulmaster)
which one of those is most appropriate for which type of simultaneous equation question , because the different variations of questions its hard to apply sometimes to my question if its different etc
i dont know if that made sense like its hard because in the question i gave numbers didn't divide properly into each other which is really confusing ?
honestly been trying understand simultaneous equations for at least 2 years at this point . i think its a hopeless situation at this point
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Sinnoh
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(Original post by hangulmaster)
which one of those is most appropriate for which type of simultaneous equation question like i mean can you apply both of those methods to any simultaneous equation and it work just as well? you know what i mean? , because the different variations of questions its hard to apply sometimes to my question if its different etc
i dont know if that made sense like its hard because in the question i gave numbers didn't divide properly into each other which is really confusing ?
honestly been trying understand simultaneous equations for at least 2 years at this point . i think its a hopeless situation at this point
It can always click. Never rule out something as being impossible to understand.
There are two ways of solving simultaneous equations. One involves eliminating one of the unknowns, the other involves a bit or rearranging and substitution.
When you are given two linear equations to solve simultaneously, then you can always use elimination

So that's when it's in this form:
ax + by = p
cx + dy = q

Provided the LHS coefficients are different, that is - otherwise, it would be like trying to find where two parallel lines intersect. But they wouldn't ask you to solve an unsolvable equation so no worries there.

In your example, -2x + y = 17
and x - y = -8

This will sound like the most obvious thing in the world, but remember that this tells you that for each row, the left hand side is equal to the right hand side.
But this is important - what would happen if you did 17 + (-8), only that instead of writing 17 + (-8), you wrote (-2x + y) + (x - y)?
Try it, see what happens.

So what about when it's in a different form?
Suppose they give you this:

-2x + y = 17
x2 - y = 9

This is as hard as they can really make it in GCSE maths. Try using the method Den987 used.
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hangulmaster
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ok so i read through the elimination part

i got a new question

y-3x=6
x-y=-8

So following the bbc steps

it says to put them in ax+by=C form

so
1) -3x+y=6
x-y=-8

2) find same co efficient is the next step right and because thwey are different sign we add them right?
so
-2x+y=-2 (then solve with inverse operations?)
x=1

3) put the x number back into equation 1
-3 x 1 + y=6
-3+y=6
then i got y=-2

which was wrong it was 9

i dont understand i followed everything??? why doesnt it work im so confused godhelpmewiththesesatanicmathspr oblems
please tell me where i went wrong and why the maths gods hate my soul

thanks
(Original post by mqb2766)
Which notes are you looking at?
Does
https://www.bbc.com/bitesize/guides/z9y9jty/revision/1
make any sense?

If so, Ill guide you through solving it using both methods. It should not take you 2 years to understand.
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mqb2766
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#10
When you add the equations you get
-2x = -2
So x=1. The using the 2nd equation
y = 8+x = ...
Or using the 1st equation
y = 6+3x = ...
Can you see this?

(Original post by hangulmaster)
ok so i read through the elimination part

i got a new question

y-3x=6
x-y=-8

So following the bbc steps

it says to put them in ax+by=C form

so
1) -3x+y=6
x-y=-8

2) find same co efficient is the next step right and because thwey are different sign we add them right?
so
-2x+y=-2 (then solve with inverse operations?)
x=1

3) put the x number back into equation 1
-3 x 1 + y=6
-3+y=6
then i got y=-2

which was wrong it was 9

i dont understand i followed everything??? why doesnt it work im so confused godhelpmewiththesesatanicmathspr oblems
please tell me where i went wrong and why the maths gods hate my soul

thanks
Last edited by mqb2766; 6 days ago
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hangulmaster
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ook yes i see how you got 9 when you arranged the equations like that

like how do you know to arrange the equation with like y=....

instead of leaving it like
-3x1+y=6 etc
because some equaitons leave it like that but now its been arranged different
because actually when you input it in that way it doesnt work by defualt maths is a confusing lie
its lying to me..
im so confused maths has too many inconsistent rules
(Original post by mqb2766)
When you add the equations you get
-2x = -2
So x=1. The using the 2nd equation
y = 8+x = ...
Or using the 1st equation
y = 6+3x = ...
Can you see this?
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mqb2766
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Don't be too suspiciois.

After you've got one of the variables (x in this case), you can use either of the two original equations. Sub the value for x, then you have a single equation in a single variable (y in this case) which can be solved.

Try doing a few more problems like this, you've made a start. Post your progress.

(Original post by hangulmaster)
ook yes i see how you got 9 when you arranged the equations like that

like how do you know to arrange the equation with like y=....

instead of leaving it like
-3x1+y=6 etc
because some equaitons leave it like that but now its been arranged different
because actually when you input it in that way it doesnt work by defualt maths is a confusing lie
its lying to me..
im so confused maths has too many inconsistent rules
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hangulmaster
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i just did a couple more questions and managed to get them correct to my great suprise since im a massive idiot
i understand the elimination methods/ process a bit more now
even though i solved iti was not 100% sure like i couldn't explain confidently what i was doing for example
i hope i get better and more confident
(Original post by mqb2766)
Don't be too suspiciois.

After you've got one of the variables (x in this case), you can use either of the two original equations. Sub the value for x, then you have a single equation in a single variable (y in this case) which can be solved.

Try doing a few more problems like this, you've made a start. Post your progress.
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mqb2766
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Thats good prpgress. Try a few more this weekend and if you want a bit more insight or help with substitution, just post.
(Original post by hangulmaster)
i just did a couple more questions and managed to get them correct to my great suprise since im a massive idiot
i understand the elimination methods/ process a bit more now
even though i solved iti was not 100% sure like i couldn't explain confidently what i was doing for example
i hope i get better and more confident
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Deggs_14
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(Original post by sunshinehss)
Lmao I solved this as well because this was my favourite thing at GCSE aka the one thing I knew I was sure to get marks on 😭😭 wanted to see if i still had it (👀 very questionable 😂)

Anyhoo I'll upload my working out in a bit
OMG I relate to this so much - I loved doing simultaneous equations 😂☹️
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hangulmaster
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what about this type of equation

x+2y=15
y=2x+3

my attempt working out

x+2y=15
y=2x+30

put in the form thing like
x+2y=15
-2x+y=30

-4x+2y=60
x+2y=15

-3x=45
x=15

??/ it was all wrong i dont understand why the answers were

x= -9
y=12
(Original post by mqb2766)
Thats good prpgress. Try a few more this weekend and if you want a bit more insight or help with substitution, just post.
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mqb2766
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Typo at start of Its +3 at the start not +30. Also when you combine ypu'd have -5x = 45. Remember you're subtracting so x=-9.

Redo the last bit and you should have it.

Note this equation was probably easier to solve using substitution, but get elimination sussed first.
(Original post by hangulmaster)
what about this type of equation

x+2y=15
y=2x+3

my attempt working out

x+2y=15
y=2x+30

put in the form thing like
x+2y=15
-2x+y=30

-4x+2y=60
x+2y=15

-3x=45
x=15

??/ it was all wrong i dont understand why the answers were

x= -9
y=12
Last edited by mqb2766; 6 days ago
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