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AS Maths Simultaneous equations Urgent Help please !

Hey so in a few days my teacher is setting us a test. So for my own benefit and revision purposes I've been doing several questions. I had a whole load of simultaneous equations question that I've been doing today. I've managed to to every single one so far until I got to the following question, I'm really confused on it and got my self into a muddle and I know my answer is wrong because it doesn't work. I've been trying for ages on this question and I would really appreciate if someone could solve this however talk me through it at the same time so I can learn from so I can complete the rest of the questions. I would be really appreciative of any help and thanks in advance to anyone who does. (Reps given)

Question

x + 3y = 16
x^2 - xy + 2y^2 = 46
Original post by Aty100
Hey so in a few days my teacher is setting us a test. So for my own benefit and revision purposes I've been doing several questions. I had a whole load of simultaneous equations question that I've been doing today. I've managed to to every single one so far until I got to the following question, I'm really confused on it and got my self into a muddle and I know my answer is wrong because it doesn't work. I've been trying for ages on this question and I would really appreciate if someone could solve this however talk me through it at the same time so I can learn from so I can complete the rest of the questions. I would be really appreciative of any help and thanks in advance to anyone who does. (Reps given)

Question

x + 3y = 16
x^2 - xy + 2y^2 = 46


Use the first equation to write x in terms of y (or y in terms of x), and then substitute the result in to the second equation. Then solve.

You shouldn't expect us to provide solutions because we're not allowed to do so.
Original post by Aty100
Hey so in a few days my teacher is setting us a test. So for my own benefit and revision purposes I've been doing several questions. I had a whole load of simultaneous equations question that I've been doing today. I've managed to to every single one so far until I got to the following question, I'm really confused on it and got my self into a muddle and I know my answer is wrong because it doesn't work. I've been trying for ages on this question and I would really appreciate if someone could solve this however talk me through it at the same time so I can learn from so I can complete the rest of the questions. I would be really appreciative of any help and thanks in advance to anyone who does. (Reps given)

Question

x + 3y = 16
x^2 - xy + 2y^2 = 46


Post your working and I'm happy to find where you've gone wrong.
Rearrange the first equation to make x = 16 - 3y, then substitute it into the quadratic (in place of x).
Then solve as you would for any other quadratic.
Reply 4
Do you know how to make x the subject or y?
so if it was 2x + 16= y
the subject would then be 2x= y -16
inorder to be a subject the letter has to be positive and by itself.
therefore the answer is x = y/2 - 8
Reply 5
Original post by Muttley79
Post your working and I'm happy to find where you've gone wrong.


Thanks,
I'm using this whiteboard app and cleared the other workings from before because I got the wrong answer but this is how I started
Is 16x16=256 not 136???
Original post by Aty100
Thanks,
I'm using this whiteboard app and cleared the other workings from before because I got the wrong answer but this is how I started


Two errors found:

16 x 16 = 256

The should be a y^2 term when you expand the first set of brackets.

I did not check further because these need to be corrected first.
Reply 8
Original post by Muttley79
Two errors found:

16 x 16 = 256

The should be a y^2 term when you expand the first set of brackets.

I did not check further because these need to be corrected first.


Omg I'm so stupid, I make really silly mistakes when I'm tired, thanks
Original post by Aty100
Omg I'm so stupid, I make really silly mistakes when I'm tired, thanks


No problem - it's hard to find your own slips when you're tired :smile:

Try again and see how it goes.
Original post by Aty100
Omg I'm so stupid, I make really silly mistakes when I'm tired, thanks


You're not stupid, just tired. Theres a website my private tutor recommended to me called the Mathematics Enhancement Program; it's a little bit old but it goes through up to A-Level material and it explains it really simply, step-by-step so you can understand it easier.
Reply 11
Original post by Muttley79
Two errors found:

16 x 16 = 256

The should be a y^2 term when you expand the first set of brackets.

I did not check further because these need to be corrected first.


I tried it again?
Reply 12
Thanks ! :smile::h:
Original post by Aty100
I tried it again?


OK so you've got a quadratic now - remember that equation = 0.

You can divide through by a common factor - I can see 7 works - then try to factorise.
(edited 8 years ago)
Reply 14
Original post by Muttley79
OK so you've got a quadratic now - remember that equation = 0.

You can divide through by a common factor - I can see 7 works - then try to factorise.


So is this correct ?
Edit : Argh it should be positive 5 & 3 I realise where I made my mistake
(edited 8 years ago)
Original post by Aty100
So is this correct ?


In your previous picture, so before you done what Muttley79 said, there was an error with your final answer.
It is meant to be: 14y^2 - 112y + 210 = 0.
Do the exact same process - solve this quadratic though.

Also, good job when you realised that there is a common divisor in the quadratic - I had a similar quadratic once and didn't know what to do lol and my quadratic equation had become so large it was too tough to solve without a calculator.
(edited 8 years ago)
Original post by Aty100
So is this correct ?


No, sorry. I have just looked back at your quadratic - where did the +y terms come from and the constant?

Your expansion is coorect now but I think collecting of like terms is incorrect.
Original post by Aty100
So is this correct ?
Edit : Argh it should be positive 5 & 3 I realise where I made my mistake


Now that's correct for the y values :P, I'm sure you will not make a mistake solving for the x values.

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