Original post by realed

Some simultaneous questions/quadratic inequality equation question i don't understand. Pls give me the answer and the explanation. I need it for my maths homework

1) y=x-3

y=x^2-3x-8

2) y=1-x

y^2-xy=0

3) x+y=7

x^2+y^2=25

4) x^2-3x-5<0

1) y=x-3

y=x^2-3x-8

2) y=1-x

y^2-xy=0

3) x+y=7

x^2+y^2=25

4) x^2-3x-5<0

Its worth having a read of the sticky at the top of the forum about not just asking for the answer/working. What have you tried to solve (any of) these? Using substituion, rather than elimination, would be a good thing to try for some of the questions. Upload what you tried?

(edited 1 year ago)

Original post by realed

Some simultaneous questions/quadratic inequality equation question i don't understand. Pls give me the answer and the explanation. I need it for my maths homework

1) y=x-3

y=x^2-3x-8

2) y=1-x

y^2-xy=0

3) x+y=7

x^2+y^2=25

4) x^2-3x-5<0

1) y=x-3

y=x^2-3x-8

2) y=1-x

y^2-xy=0

3) x+y=7

x^2+y^2=25

4) x^2-3x-5<0

Like @mqb2766 said, there's little point in us giving you the answers. You won't be learning anything, and we will be doing you a disservice when it comes to the exams. The homework is there to prepare you for the exams and coursework, not to be an inconvenience.

However, I won't leave you hanging and not offer any help. If you understand the basic principles of quadratic equations, simultaneous equations, and inequalities, then you're missing the problem solving aspect of it.

Each of these problems involves at least one of the following steps:

1) move everything to one side and leave one side = 0 (a principle from quadratic equations)

2) factorise the quadratic

3) square and expand the quadratic

4) substitute one of the equation into the other (a defining feature of simultaneous equations)

5) flip the inequality

These steps won't be in order and the questions won't all involve the same order of steps. You would need to think through these questions. Maths is partly about solving problems, and you're refining your problem solving skills.

Original post by MindMax2000

Like @mqb2766 said, there's little point in us giving you the answers. You won't be learning anything, and we will be doing you a disservice when it comes to the exams. The homework is there to prepare you for the exams and coursework, not to be an inconvenience.

However, I won't leave you hanging and not offer any help. If you understand the basic principles of quadratic equations, simultaneous equations, and inequalities, then you're missing the problem solving aspect of it.

Each of these problems involves at least one of the following steps:

1) move everything to one side and leave one side = 0 (a principle from quadratic equations)

2) factorise the quadratic

3) square and expand the quadratic

4) substitute one of the equation into the other (a defining feature of simultaneous equations)

5) flip the inequality

These steps won't be in order and the questions won't all involve the same order of steps. You would need to think through these questions. Maths is partly about solving problems, and you're refining your problem solving skills.

However, I won't leave you hanging and not offer any help. If you understand the basic principles of quadratic equations, simultaneous equations, and inequalities, then you're missing the problem solving aspect of it.

Each of these problems involves at least one of the following steps:

1) move everything to one side and leave one side = 0 (a principle from quadratic equations)

2) factorise the quadratic

3) square and expand the quadratic

4) substitute one of the equation into the other (a defining feature of simultaneous equations)

5) flip the inequality

These steps won't be in order and the questions won't all involve the same order of steps. You would need to think through these questions. Maths is partly about solving problems, and you're refining your problem solving skills.

thx for your advice i looked at the answers again and realised that i made a couple of mistakes with my working. With 1 you have to move everything to 1 side,Then factorise it to work out x. x-3= x^2-3x-8

0=x^2-4x-5

(x+1)(x+5)= x= -1 or -5/ y=2 or -4

For number 2 it's y=1-x

y^2-xy=0

so step 1 is to factorise the second one y(y-x)

Then you put the values in (1-x)(1-x-x)=(1-x)(1-2x)

x=1 or 0.5 so as y=1-x y is 0 or 0.5

3) With this one you have to choose a specific value.

x+y=7

x^2+y^2=25

y=7-x

(7-x)^2+x^2=2x^2-14x+49=24

2x^2-14x+24=0

x^2-7x+12=0

x^2-3x-4x+12

(x-3)(x-4)

x=3 or x=4

y=4 or y=3

However i completly don't understand what you mean when you say flip the inequality can you tell me what it means and give me an example pls

Original post by realed

thx for your advice i looked at the answers again and realised that i made a couple of mistakes with my working. With 1 you have to move everything to 1 side,Then factorise it to work out x. x-3= x^2-3x-8

0=x^2-4x-5

(x+1)(x+5)= x= -1 or -5/ y=2 or -4

For number 2 it's y=1-x

y^2-xy=0

so step 1 is to factorise the second one y(y-x)

Then you put the values in (1-x)(1-x-x)=(1-x)(1-2x)

x=1 or 0.5 so as y=1-x y is 0 or 0.5

3) With this one you have to choose a specific value.

x+y=7

x^2+y^2=25

y=7-x

(7-x)^2+x^2=2x^2-14x+49=24

2x^2-14x+24=0

x^2-7x+12=0

x^2-3x-4x+12

(x-3)(x-4)

x=3 or x=4

y=4 or y=3

However i completly don't understand what you mean when you say flip the inequality can you tell me what it means and give me an example pls

0=x^2-4x-5

(x+1)(x+5)= x= -1 or -5/ y=2 or -4

For number 2 it's y=1-x

y^2-xy=0

so step 1 is to factorise the second one y(y-x)

Then you put the values in (1-x)(1-x-x)=(1-x)(1-2x)

x=1 or 0.5 so as y=1-x y is 0 or 0.5

3) With this one you have to choose a specific value.

x+y=7

x^2+y^2=25

y=7-x

(7-x)^2+x^2=2x^2-14x+49=24

2x^2-14x+24=0

x^2-7x+12=0

x^2-3x-4x+12

(x-3)(x-4)

x=3 or x=4

y=4 or y=3

However i completly don't understand what you mean when you say flip the inequality can you tell me what it means and give me an example pls

One thing Id always do for questions like these is a quick sketch of the functions.

1) is a line intersecting a quadratic

2) intersection of two lines, apart from when y=0

3) a line intersecting a circle and the solutions being well known pythagorean triplets

4) the region where a quadratic is below the x-axis. There isnt really a need to flip the inequality, but you may need to use the formula to get the roots.

Some solutions seem are ok - x values for 1 - typo? Its easy to sub back into the equations to verify. Also when listing your values, give the (x,y) pairs otherwise the 2*2 values can be combined in 4 ways, 2 of which are correct.

(edited 1 year ago)

Original post by realed

thx for your advice i looked at the answers again and realised that i made a couple of mistakes with my working. With 1 you have to move everything to 1 side,Then factorise it to work out x. x-3= x^2-3x-8

0=x^2-4x-5

(x+1)(x+5)= x= -1 or -5/ y=2 or -4

For number 2 it's y=1-x

y^2-xy=0

so step 1 is to factorise the second one y(y-x)

Then you put the values in (1-x)(1-x-x)=(1-x)(1-2x)

x=1 or 0.5 so as y=1-x y is 0 or 0.5

3) With this one you have to choose a specific value.

x+y=7

x^2+y^2=25

y=7-x

(7-x)^2+x^2=2x^2-14x+49=24

2x^2-14x+24=0

x^2-7x+12=0

x^2-3x-4x+12

(x-3)(x-4)

x=3 or x=4

y=4 or y=3

However i completly don't understand what you mean when you say flip the inequality can you tell me what it means and give me an example pls

0=x^2-4x-5

(x+1)(x+5)= x= -1 or -5/ y=2 or -4

For number 2 it's y=1-x

y^2-xy=0

so step 1 is to factorise the second one y(y-x)

Then you put the values in (1-x)(1-x-x)=(1-x)(1-2x)

x=1 or 0.5 so as y=1-x y is 0 or 0.5

3) With this one you have to choose a specific value.

x+y=7

x^2+y^2=25

y=7-x

(7-x)^2+x^2=2x^2-14x+49=24

2x^2-14x+24=0

x^2-7x+12=0

x^2-3x-4x+12

(x-3)(x-4)

x=3 or x=4

y=4 or y=3

However i completly don't understand what you mean when you say flip the inequality can you tell me what it means and give me an example pls

Sorry, I wasn't thinking far ahead enough regarding the inequality, so @mqb2766 is correct. You don't need to do anything to the inequality, but you will need to know what the viable regions are (usually a graph will help) based on the inequality like he/she outlined.

He is also correct regarding the typo. Try working a little slower to avoid careless mistakes.

- GCSE Exam Discussions 2024
- TSR Study Together - STEM vs Humanities!
- Alevel combination (urgently needs help)
- I have a lot OF A-level and GCSE Maths and Further Maths resources. Who's Interested?
- A level choices for imperial?
- a level maths
- A Level FM in one year or two
- Any good revision resources/ websites for GCSE?
- Acturial science
- A level further maths worth it
- Economics degree
- Resitting year 12
- Maths vs Maths and Physics
- Cambridge university natural sciences
- Should A-level Maths or A-level Statistics be compulsory?
- Further Maths GCSE
- maths a level
- Should I stick to Foundation Maths GCSE or move to Higher Tier??
- How important is maths in a-level physics?
- Will universities accept maths and further maths as two?

Last reply 3 minutes ago

2024 entry A100 / A101 Medicine fastest and slowest offer sendersMedicine

860

Last reply 3 minutes ago

Official Cambridge Postgraduate Applicants 2024 ThreadLast reply 3 minutes ago

Can I drop out of college once I have an unconditional uni offer?Last reply 4 minutes ago

What do I need - I've a UK passport but live in EULast reply 6 minutes ago

Oxford Economics Degree ApprenticeshipLast reply 7 minutes ago

My boyfriend left me because he said my breasts and butt were too smallLast reply 7 minutes ago

Children to no longer be prescribed puberty blockers, NHS England confirmsLast reply 9 minutes ago

Is mental health nursing paid for by the government at UOMLast reply 10 minutes ago

Official UCL Offer Holders Thread for 2024 entryPosted 10 minutes ago

BTEC level 3 certificate in performing artsLast reply 11 minutes ago

Official University of Edinburgh Offer Holders Thread for 2024 entryLast reply 11 minutes ago

anyone else waiting on LSE law?Last reply 12 minutes ago

Official London School of Economics and Political Science 2024 Applicant ThreadLast reply 13 minutes ago

Official: University of Nottingham A100 2024 Entry Applicant threadLast reply 15 minutes ago

Goldmansachs Degree Apprenticeship 2024Last reply 16 minutes ago

Inlaks, Commonwealth, and Other Scholarships for Indian Students 2024: ThreadLast reply 18 minutes ago

Official University of Bristol Offer Holders Thread for 2024 entryLast reply 1 week ago

Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths

71

Last reply 1 week ago

Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths

71