I'm having trouble with these questions:

If given a linear system:

$\displaystyle (m-2)x+y=2$

and

$\displaystyle mx+2y=k$

For which values of m and k (unique values or certain sets of values) are the following true:

1: The system has unique solutions

2: The system has no unique solutions

3: There are infinitely many solutions

Or, consider the system of three equations:

$\displaystyle 2x+ay-z=0$

$\displaystyle 3x+4y-(a+1)z=13$

$\displaystyle 10x+8y+(a-4)z=26$

For what values of a are the same three conditions above satisfied?

Also, what techniques are used to do these questions in general?

Thanks for all the help in advance