Thanks Alan

Hi Braksess,

I really like your dogged determination to understand this!

I think you are having problems with this

$$xy-x=x(y-1)$$

so that is the bit I am going to look at.

Look at the rectangle below.     

The area of the whole rectangle is      $$x\times y \quad units^2$$

I have cut a little rectangle off the end.  The area of the cut off bit is   $$1\times x=x \quad units^2$$

so the area that is left when you take away the litle bit at the end is  

 $$\\x\times y - x\\
or\; just\\ xy-x$$

The area that is left after you take away the bit at the end is displayed in yellow below.

The length of the top is y-1  (because 1 unit was cut off)

The side is still x  units

The area is   x(y-1)

SO          $$xy-x=x(y-1)$$

LETS look at it the other way around

you probably know that     3(x-1)=3*x-3*1 = 3x-3

It works with letters too

$$x(y-1)=x\times y - x\times 1 = xy-x$$

NOW lets look at how to factorise it going in the other direction.

$$\\xy-x=x\times y - x\times 1\\
$x is a common factor so we can factor it out and we will be left with $y-1$ in the bracket.$\\
=x(y-1)$$

$$\\1.5x - y = -2 \qquad (1a)\\
-5x + 4y = 14 \quad (2a)\\
(1a)*4\\
6x-4y=-8 \qquad (1b)\\
(2a)+(1b)\\
-5x+6x+4y+-4y=14+-8\\
x=6\\\\
$sub x=6 into (1a) to find y$\\
1.5*6-y=-2\\
9-y=-2\\
-y=-11\\
y=11\\
$so the solution is x=6 and y=11$$$

Cause not Dragon.      thanks for the point.   

@@ End of Day Wrap            Mon 13/10/14 Sydney,            Sydney,  Australia Time 11:55pm     ♬

Good evening folks,

I like the weekends they are a lot quieter.  It is late Monday night here but for many of you Monday has only really just begun.

Our wonderful answerers are Rosala, Geno3141, CPhill and Alan.  Thank you all.  

Here are the interest posts:

1) Light fun with numbers.

Tues 13/10/14

1) Algebra concepts   Thanks Geno, Chris and Melody.

Echidna

Chris was laughing about my word "porkies"

Porkies is a shortened version of "pork pies"

Austalians used to be very into rhyming slang.  Pork pies rhymes with lies.

So if you are telling pork pies (or porkies)  then you are telling lies.

I am told that we adopted rhyming slang from the Brits.  (Engish)

Perhaps Alan knows more about this.      

-------------------

Also monotremes are mammals that lay eggs.

An echidna lays eggs but still feeds its baby with milk.

There are only 2 monotremes in the whole world.   The platypus and the echidna.  Both are native to Australia.

The male platypus has poisonous spurs on its back legs.  I just looked this up and I was very surprised to find that there are a lot of mammals that produce poison.  There is even a small primate in vietnam that produces poison.  How about that!    

Hi Rosala,

The US people have their whole day in front of them and my day is almost at an end.    :)

You are one of the few who is in the middle of their day.