Unique solutions

[1i1ii1i]

The simultaneous linear equations
kx-3y=O
5x-(k+2)y=0
where k is a real constant, have a unique solution?

what is meant by a unique solution and how do i do this?

[Phy124]

The simultaneous linear equations
kx-3y=O
5x-(k+2)y=0
where k is a real constant, have a unique solution?

what is meant by a unique solution and how do i do this?

Unique solution: When the two cross at a single point
Infinite solutions: When the two lines are of the same equations and at ever x value the y value is the same for both
No solution: When the two lines are parallel and do not touch

To find a unique solution, the determinant cannot be equal to zero i.e.















Or in other terms(correct way of writing it):



edit: fixed a mistake I found

[1i1ii1i]

thankx alot, and why can't the determinant to equalto 0

[TrueTears]

if it did, then the reduced row echelon form of the above system of linear equations will either yield infinitely many solutions or no solutions.

[b^3]

@Phy124

Code: [Select]

k\in R{-5,3}
EDIT: NVM you fixed it.

[yawho]

if it did, then the reduced row echelon form of the above system of linear equations will either yield infinitely many solutions or no solutions.

Are you helping or confusing? Please use terms and definitions used in year 12.

[TrueTears]

ok.

[iirene]

My methods teacher taught me another way...

Given the two equations with two unknowns:
a₁x + b₁y = c₁
a₂x + b₂y = c₂

For one solution (unique):


For no solutions:


For infinite solutions:



So in terms of your question, it would be


             (cross multiplied)





Therefore, for a unique solution, as Phy124 said...

[paulsterio]

if it did, then the reduced row echelon form of the above system of linear equations will either yield infinitely many solutions or no solutions.

Are you helping or confusing? Please use terms and definitions used in year 12.

How else do you want him to say it?
He was asked why the determinant cannot equal zero.
He answered that the reduced row echelon form (i.e. solution form) of the linear equations would yield infinitely many solutions or no solutions
I don't see what the issue is, especially considering that you weren't even the one who asked the question.

To say it in your own words:
Are you confused or being annoying? Please be respectful and don't be so accusatory.

[yawho]

if it did, then the reduced row echelon form of the above system of linear equations will either yield infinitely many solutions or no solutions.

Are you helping or confusing? Please use terms and definitions used in year 12.

How else do you want him to say it?
He was asked why the determinant cannot equal zero.
He answered that the reduced row echelon form (i.e. solution form) of the linear equations would yield infinitely many solutions or no solutions
I don't see what the issue is, especially considering that you weren't even the one who asked the question.

To say it in your own words:
Are you confused or being annoying? Please be respectful and don't be so accusatory.

I have just finished the topic and I have never heard of the term used by my teacher.

[paulsterio]

I have just finished the topic and I have never heard of the term used by my teacher.

So you've never described a system as having infinitely many solutions or no solutions? I've been hearing of that since Year 8?

[yawho]

I have just finished the topic and I have never heard of the term used by my teacher.

So you've never described a system as having infinitely many solutions or no solutions? I've been hearing of that since Year 8?

Yes I have heard and used 'infinitely many solutions or no solutions', but not 'the reduced row echelon form'. So why not just say solution form?

[paulsterio]

Yes I have heard and used 'infinitely many solutions or no solutions', but not 'the reduced row echelon form'. So why not just say solution form?

It's irrelevant though, you can say whatever you want, but the key words are that it's got infinitely many or no solutions.

[Phy124]

Yes I have heard and used 'infinitely many solutions or no solutions', but not 'the reduced row echelon form'. So why not just say solution form?

Well, in my opinion, it's not as though you needed to understand it anyway. If you were to take that out, you essentially have an answer you should be able to comprehend, anyway.

if it did, then the reduced row echelon form of the above system of linear equations will either yield infinitely many solutions or no solutions.

TT structured his answer in a way that both average and accelerated (Ambiguous, but I can't be bothered changing words) students would be able to interpret.

[yawho]

Yes I have heard and used 'infinitely many solutions or no solutions', but not 'the reduced row echelon form'. So why not just say solution form?

It's irrelevant though, you can say whatever you want, but the key words are that it's got infinitely many or no solutions.

Of course it is relevant. If one tries to explain why would one use a different 'language' to cause confusion?