VCE Methods Question Thread!

[zvezda]

in the essentials book, example 9 (just before the start of Ex 2F), it goes through some steps describing how to solve, and it says "using a CAS calculator to find the solution".
With these types of qs (eg Ex 2F q4), would we need to know how to do it by hand ?

[zvezda]

Also with 2F, it pretty much revolves around example 9, and for some reason, my brain just wont link things together.
For example, q5, I set it up in matrix form and worked throuh figuring out the values of m given that the determinant is 0. I ended up with m= -5 or 3. Now I have no idea what to do with these values, do I just sub them back in to the equations to see which one gives me infinite solutions and which one gives me no solutions to the 2 linear equations???

Also, I entered the 2 equations into my calculator and got:
x= (m-5)/(m-3) and y=2/(m-3).
What would I do from there???
how on earth would you get m=-5 for infinite solutions using those 2 solutions in terms of m???^^
Im so lost

[zvezda]

Is there a way of working out whether there no infinite or no solutions without simply plugging in m values into the equations for the sake of trial and error ??

[Will T]

Stef you're right on the money.

The values of m are correct, substitute them into the original system of equations and see which m value gives you:

The same equation for both lines

Or

Two equations of parallel lines (same gradient) with differing y-intercepts.

Obviously the former implies infinite solutions and the latter implies no solutions.

As with the CAS, I'm not sure what you're rambling about.

[zvezda]

cheers will. solve the eqns in terms of m, then what?

[Will T]

Let's just double check we're on the same metaphorical page here.

For infinite solutions to exist or for no solutions to exist the following criteria must be satisfied: the determinant of the matrix of coefficients must equal zero.

So now that we know that, it becomes clear after a little bit of algebra that m has to equal -5 or 3.

But we need to know which corresponding value of m gives infinite solutions and which gives no solutions. It's going to be -5 for one and 3 for the other, we just have to find out which is which. The only way to do this that I can think of/is practical is to substitute the values of m back into the original system of equations. Yes it is a bit of trial and error, that's life. (C'est la vie as the French say).

I don't get what you mean when you say solve the equations in terms of 'm' that is not at all what you need to do.

[abcdqd]

@Will T
7 subjects next year? holy shit bro LOL

[TrueTears]

ye u dont need to trial and error if you don't want to, if the augmented coefficient matrix has a row of zeros in its reduced echelon form, ie, after applying algebra to solve for each variable, then you have infinite solutions, if it has a row of zeros but the last number is a non-zero value, then it has no solutions

if youre having trouble with this, i suggest you read elementary linear algebra by anton, standard lin.alg text

[zvezda]

Let's just double check we're on the same metaphorical page here.

For infinite solutions to exist or for no solutions to exist the following criteria must be satisfied: the determinant of the matrix of coefficients must equal zero.

So now that we know that, it becomes clear after a little bit of algebra that m has to equal -5 or 3.

But we need to know which corresponding value of m gives infinite solutions and which gives no solutions. It's going to be -5 for one and 3 for the other, we just have to find out which is which. The only way to do this that I can think of/is practical is to substitute the values of m back into the original system of equations. Yes it is a bit of trial and error, that's life. (C'est la vie as the French say).

I don't get what you mean when you say solve the equations in terms of 'm' that is not at all what you need to do.

solving the equations in terms of m is one of the steps they used in essentials to explain how to solve. im just gonna ignore essentials, sometimes their explanations are completely useless and not at all user friendly. Dont get started on the french lol

Cheers TrueTears. Although, is that on the methods course or something beyond it?

[zvezda]

With parameters and solving simultaneous equations with them, is it always necessary to either let y=parameter (for 2 eqns) or z=parameter (3 eqns)? what if i decided to just let x equal the parameter? its a trend that is present in essentials so i dont know if its in some way compulsory or not

[Limista]

With parameters and solving simultaneous equations with them, is it always necessary to either let y=parameter (for 2 eqns) or z=parameter (3 eqns)? what if i decided to just let x equal the parameter? its a trend that is present in essentials so i dont know if its in some way compulsory or not

x, y or z can be the parameters. It does not matter.

[zvezda]

yeah i know but im just wondering whether theres some compulsory thing. Thanks.
Also, why do we use parameters? I came across this question in essentials textbook:

Find all solutions of:
and

Is this the reason why we use parameters??

[Limista]

yeah i know but im just wondering whether theres some compulsory thing. Thanks.
Also, why do we use parameters? I came across this question in essentials textbook:

Find all solutions of:
and

Is this the reason why we use parameters??

There's no compulsory thing. I know that the essentials textbook does that, since I used it last year in fact and also asked my teacher the same question 

We use parameters if there are going to be infinite solutions. When are there infinite solutions?
* if you've got more variables to solve for, than you have equations to solve with (and thus, you will have to use replace one of the variables with a parameter)

Yup - the example you've given above is perfect for knowing that you need to use a parameter in order to be able to find x, y and z

edit: I also realized that we're doing the exact same subjects! ...except you're doing French and I'm doing German 

[TrueTears]

yeah i know but im just wondering whether theres some compulsory thing. Thanks.
Also, why do we use parameters? I came across this question in essentials textbook:

Find all solutions of:
and

Is this the reason why we use parameters??

You've been using parameters all along, it's just that you haven't realised it. Eg, you have most likely manipulated a quadratic's parameters before, f(x)=ax^2+bx+c, x is the argument and a, b and c are the parameters

[zvezda]

There's no compulsory thing. I know that the essentials textbook does that, since I used it last year in fact and also asked my teacher the same question 

We use parameters if there are going to be infinite solutions. When are there infinite solutions?
* if you've got more variables to solve for, than you have equations to solve with (and thus, you will have to use replace one of the variables with a parameter)

Yup - the example you've given above is perfect for knowing that you need to use a parameter in order to be able to find x, y and z

edit: I also realized that we're doing the exact same subjects! ...except you're doing French and I'm doing German 

well as they say, great minds think alike lol. cheers for the help. So you did psych last year? howd you go?

You've been using parameters all along, it's just that you haven't realised it. Eg, you have most likely manipulated a quadratic's parameters before, f(x)=ax^2+bx+c, x is the argument and a, b and c are the parameters

ah interesting, never knew. thanks