This is METH-ness! (H/w help trend).

[the.watchman]

Ok

Let d be the distance on freeway

(1)

AND (where is the distance on country roads and is the time on country roads)

(2)

sub (1) into (2):



,

[brightsky]

Let the distance spent on the freeway be km.

So journey spent on country roads would be km.

Let hours be the time spent on the freeway.

So the time spent on country roads would be hours.

(1)

(2)

Substitute (1) into (2):



Substitute back into (1):



EDIT: Beaten!

[the.watchman]

LOL, two things:

1. We don't need to find d

2. If you find t first, I assure you it's less working

Good job anyway!

[brightsky]

LOL, two things:

1. We don't need to find d

2. If you find t first, I assure you it's less working

Good job anyway!

LOL, hehe, woops! Blame the time! It's 10:28 pm and I'm tired! :p

[Ilovemathsmeth]

Actually that question only appears confusing. It's solution is so simple that I thought it was a trick question

[Momo.05]

Hrmm, this is a matrix related question Im quite stuck on, please help !

Find the value of m for which the simultaneous equations;

(m+3)x + my = 12
(m-1)x + (m-3)y = 7

have no solutions .

Thank-you

[cipherpol]

Ok, so if we put it into a matrix we get something like:

 m+3    m
 m-1    m-3

So for no solutions we require that the determinant=0.







for no solutions.

[Momo.05]

OH, the det has to equal 0 for no solutions ..?
Guess i missed that
THANK YOU

[brightsky]

OH, the det has to equal 0 for no solutions ..?
Guess i missed that
THANK YOU

When the determinant = 0, there can be both no solutions or infinitely many solutions. Just need to sub values back in to check which one it is.

[Momo.05]

Ohhh, i see.
Thanks for the heads up, i thought when the det = 0 it just mean no solutions ..
But its all done now, just going to put that note down

[the.watchman]

Graphically speaking, the two lines have the same gradient when the determinant is equal to 0

Therefore, if their y-intercepts are the same, then there are infinite solutions.
Or if they are different, no solutions.

[brightsky]

Hey, random question, what is the difference between differentiating and differentiating with respect to x?

[brightsky]

Graphically speaking, the two lines have the same gradient when the determinant is equal to 0

Therefore, if their y-intercepts are the same, then there are infinite solutions.
Or if they are different, no solutions.

Yep, so imagine two parallel lines. If the two parallel lines have the same equation, then the two lines would be the same, and hence there are infinite solutions. But if the parallel lines are apart, they will never intersect, hence no solutions.

[the.watchman]

Hey, random question, what is the difference between differentiating and differentiating with respect to x?

If you differentiate, I think is has to be with respect to a variable, eg. x

Hence why the joke referring to , it actually equals 0

[TrueTears]

Not if y = x