I need some help understanding some concepts (long post)

Okay, my professor hasn't been very reliable and my midterm is on thursday so this is the only place where I can get help.

The first concept is solving variable to systems where the variable have unique, no and infinite solutions.

Here's an example:

*For which a, b does the following system:*

*3x-y=b*

*7x+ay=1*

*have i) unique solution ii) infinite solutions iii) no solution?*

The second concept (two parts) is of linear matrices.

Here are examples:

*1) Solve the system:*

*3x+2y-z=-15*

*6x+2y+6z=22*

*-12x-8y+4z=60*

Now, I know for this question we want to get the matrix to be in reduced echelon form. My question for this is: Is there any specific method I should be using to do this or should I treat it as a puzzle?

*2) Write a system of linear equations that has the following matrix as its augmented matrix*

( 0 1 0 -1 2 3 7)

(7 3 2 2 1 2 0)

(1 2 -1 0 0 0 0)

(sorry, thats the best I could do to make it pretty)

Any help and links would be greatly appreciated.