I ended up with:
I chose option A and option D as being true... but got it wrong. Could someone possibly take a look please?
Edit (Times 2):
You know, I'm looking at this again and I'm noting that we may use equations 1 and 3 to come up with a new equation in just b and d, which we may use together with the second equation to get values for b and d unambiguously. Then note that if we are to be able to get a consistent solution equations 1 and 3 must be the same (as a and c both have the same coefficients.) So we can only find one of them.
Thus there is one free parameter, either a or c.
-Dan
PS Sorry about all the edits!
Zeez, I don't get what "parameter" means here.
When a +3c = 8 is the last standing equation, does that have one parameter or two parameters?
Combine Eq.(1) and Eq.(3) by subtracting (3) from (1), and you get
b -2d = -4 -------------(4)
Play with (2) and (4), and you'd get
b = 6
d = 5
Plug those into (1), and you'd get (1*) = (3)
3a +9c = 24
Reduce that to its simplest/lowest form,
a +3c = 8 --------***
Umm, I think that should be of two parameters.
Therefore, options A,D,E should be the answer.