Simulation equations with a quadratic Watch

Steve445
Badges: 12
Rep:
?
#1
Report Thread starter 1 week ago
#1
2x^2-y^2=31
x+3y=1


So have I rearranged the second equation correctly? I have done: 3y=1-x
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#2
Report 1 week ago
#2
(Original post by Steve445)
2x^2-y^2=31
x+3y=1
Ok, so you know what the first step is?
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#3
Report 1 week ago
#3
(Original post by Steve445)
So have I rearranged the second equation correctly? I have done: 3y=1-x
You're not wrong, but you're also not quite there with this.

Whenever we solve two equations simultaneously, we are effectively looking for a solution(s) (x,y) which satisfy both equations at once. Graphically, these are the coordinates where the two equations intersect each other. At the point of intersection, the y-coordinates are the same, and the x-coordinates are the same.

Since we know that the y-coordinates are the same, this means that y in 2x^2-y^2=31 is exactly the same as the y in x+3y = 1. This means if you can rearrange the second equation for y on its own, then you can substitute that into the first equation and obtain a relation that x solely must satisfy.

So far, you have found what 3y is, but you need to know what y on its own is. So what's one more step??


Also, as a side note, you may be used to 'rearranging for y and subbing it into the other equation' type of approach, but I also said that the x-coordinates are the same. So there is nothing stopping you from rearranging the second equation for x instead and subbing that into the first equation. In fact, this is a much simpler alternative than that which you are doing because we avoid fractions this way and the algebra is less messy hence making less room for error.
0
reply
Steve445
Badges: 12
Rep:
?
#4
Report Thread starter 1 week ago
#4
(Original post by RDKGames)
Ok, so you know what the first step is?
I know how to do the rest, but was my first bit correct

Edit: Nvm
0
reply
Steve445
Badges: 12
Rep:
?
#5
Report Thread starter 1 week ago
#5
Name:  IMG_20190312_212753.jpg
Views: 4
Size:  98.7 KB
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#6
Report 1 week ago
#6
(Original post by Steve445)
...
That's wrong.

You substituted in 3y = 1-x for y when you should've substituted in y = \dfrac{1-x}{3} instead.
0
reply
Steve445
Badges: 12
Rep:
?
#7
Report Thread starter 1 week ago
#7
(Original post by RDKGames)
That's wrong.

You substituted in 3y = 1-x for y when you should've substituted in y = \dfrac{1-x}{3} instead.
Oh, okay... So what I did was completely wrong?
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#8
Report 1 week ago
#8
(Original post by Steve445)
Oh, okay... So what I did was completely wrong?
No, you just subbed in the wrong thing. The method is fine.
0
reply
idontkn
Badges: 13
Rep:
?
#9
Report 1 week ago
#9
Why not rearrange and get x to be the subject? And then plug that in to the quadratic.
1
reply
xAikx
Badges: 12
Rep:
?
#10
Report 1 week ago
#10
Would of been easier here to make x the subject of the second equation.

So x = 1 - 3y.

You can then substitute this expression for x in your first equation and solve for your possible values for x.

From there you can find y.
0
reply
Steve445
Badges: 12
Rep:
?
#11
Report Thread starter 1 week ago
#11
So confusing man.
0
reply
Steve445
Badges: 12
Rep:
?
#12
Report Thread starter 1 week ago
#12
How can stupid examiners expect you to do this on the new spec???
0
reply
Steve445
Badges: 12
Rep:
?
#13
Report Thread starter 1 week ago
#13
Edexcel - "we are the most easiest exam board"
Me - Yeah, yeah, sure you are.
0
reply
Steve445
Badges: 12
Rep:
?
#14
Report Thread starter 1 week ago
#14
And why is it that when I look online on how to do similar questioqu like this nothing comes up?
0
reply
xAikx
Badges: 12
Rep:
?
#15
Report 1 week ago
#15
(Original post by Steve445)
And why is it that when I look online on how to do similar questioqu like this nothing comes up?
This kind of simultaneous equation is actually civered in AS maths so maybe try looking at AS maths resources in this topic
Posted on the TSR App. Download from Apple or Google Play
0
reply
Muttley79
Badges: 19
Rep:
?
#16
Report 1 week ago
#16
(Original post by Steve445)
How can stupid examiners expect you to do this on the new spec???
This is not a new topic - it's been in the GCSE for ages, I would rearrange the second equation for x as it avoids fractions.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Solent University
    Postgraduate and Professional Open Evenings Postgraduate
    Mon, 25 Mar '19
  • Cardiff University
    Undergraduate Open Day Undergraduate
    Wed, 27 Mar '19
  • University of Portsmouth
    Postgraduate and Part-Time Open Evenings Postgraduate
    Wed, 27 Mar '19

Where do you need more help?

Which Uni should I go to? (149)
18.53%
How successful will I become if I take my planned subjects? (79)
9.83%
How happy will I be if I take this career? (136)
16.92%
How do I achieve my dream Uni placement? (114)
14.18%
What should I study to achieve my dream career? (79)
9.83%
How can I be the best version of myself? (247)
30.72%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise