maths help please: linear and quadratic equation help

[rutabowa]

I need your maths help. I'm refreshing knowledge on GCSE maths.

I'm solving linear and quadratic equations. I know the correct way to do it, and got 2 answers as I should, but then I was messing around with the equations and discovered something I can't properly explain. I must have made an obvious mistake but I can't see it:

So say the 2 equations are: a=b+4 and a=bsquared + 4b. You get the right two answers, by substituting the linear exression into the quadratic equation then factorising it to equal zero (x=1 or x=-4).

But then I tried doing it the other way round, by factorising the quadratic one first, so you get a=b(b+4) right? Then if you substitute that into the linear one you get b(b+4)=b+4. So then b=(b+4)/(b+4), i.e. b=1. I.e. you only get one answer. Where have I made a mistake here?

 

[gosub]

a=b+4 = b^2+4b - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

 

[rutabowa]

Thank you, I understand how to work it out, and that there are definitely 2 answers, and that page shows that I didn't make any mistakes in factorising. What I can't explain algebraically is why b(b+4)=(b+4) doesn't ONLY simplify to 1. Because if you divide both sides by (b+4) you end up with b=(b+4)/(b+4), and any number divided by itself =1 which would give only b=1 as the answer.

 

[mauvais]

and any number divided by itself =1

Not zero, though.

 

[Crispy]

Because when b=-4, b+4=0
divide by 0 and get 0

 

[Ted Striker]

You can get one answer, IIRC? Graphically, the curve just touches the straight line, not bisecting up and down

 

[rutabowa]

Not zero, though.

RIGHT that is what I needed! so every number divided by itself is one EXCEPT zero, I knew there was some obvious thing I was missing.

Never tell your kids "every number divided by itself is always 1", it is a fucking LIE.

 

[rutabowa]

You can get one answer, IIRC? Graphically, the curve just touches the straight line, not bisecting up and down

No there's def two answers.

 

[mauvais]

b(b+4) = b+4

could be represented as

b=(b+4)/(b+4)

which gives you a divide-by-zero problem, but it's also:

b(b+4) - 4 = b

which does not.

 

[2hats]

any number divided by itself =1

0/0

 

[rutabowa]

b(b+4) = b+4

could be represented as

b=(b+4)/(b+4)

which gives you a divide-by-zero problem, but it's also:

b(b+4) - 4 = b

which does not.

Right.... I just wanted to be able to explain if my kid did end up arranging it as b=(b+4)/(b+4) why it is not wrong algebraically, and why there are still 2 possible answers.

 

[rutabowa]

Dividing by zero?

Main site: http://www.misterwootube.com Second channel (for teachers): http://www.youtube.com/misterwootube2Connect with me on Twitter (http://twitter.com/mi...

www.youtube.com