1. The problem statement, all variables and given/known data
I'm trying to solve #1 here:
http://www.student.math.uwaterloo.ca/~math115/Exams/M115.FE.pdf [Broken]

The problem is:

3. The attempt at a solution
(a) At a=2, the slope is the same. I figure any value but 2 gives unique solutions. But I don't know if this is right.
(b) At a=2, the slopes are the same, but lines are different. I cannot find any value of a that would give the same slope and same outputs for inputs of x. DNE is the answer?
(c) At a=2, there are no solutions for the system because the lines are parallel to each other. a=2 is the answer.
(d) I think this part was done correctly. I used substitution and solved for the x and y values at a=1 and resulted with (2/3, 1/3)

I would like to know about a, b, and c. I don't know if I did these right.

(d) is right, but (c) is wrong. At a = 2, you have this system:
x + 2y = 1
2x + 4y = 2
Parallel lines have the same slope, but different y-intercepts. Is that the case here?

For c), there are many solutions corresponding to x = t and y = 1 - 2t for any value of t.
For a) and b) you need to use determinants and check for possibilities of inconsistent solutions.

Do you know about determinants and their relationship to such questions? If so, use a determinant; you will see that there is a critical value of 'a' that you have missed.