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x=0.045 (45 recurring)

10x = 0.45 (45 recurring)

100x = 4.54 (54 recurring)

1000x = 45.45 (45 recurring)

To get rid of the decimals:

<...

We have two algebraic equations and we are trying to find what a and b can equal to fit for both situations. 

1. 6a + b = 16

2. 5a - 2b = 19

The easiest method...

This is simplified by solving common terms (the x's and the y's). Where X and Y terms can't be solved together.

Splitting it up:  

You can see 2x-x= x

and for ...

'Factorise' essentially means put into a simpler form, in this case with two sets of linear equations which would multiply out to give the quadratic equation shown above.

What we are look...

The question can be broken into two steps, 

1) dy/dx is asking to differentiate y=x³+5x+3 with respect to x

Differentiating we multiply by the current power and l...