1. ## Solving Systems #2

I ended up with:

$\displaystyle a = -3c + \frac{2}{7}d + \frac{46}{7}$
$\displaystyle b = \frac{8}{7}d + \frac{2}{7}d$
$\displaystyle d = \frac{13}{11}$

I chose option A and option D as being true... but got it wrong. Could someone possibly take a look please?

2. Originally Posted by Thomas

I ended up with:

$\displaystyle a = -3c + \frac{2}{7}d + \frac{46}{7}$
$\displaystyle b = \frac{8}{7}d + \frac{2}{7}d$
$\displaystyle d = \frac{13}{11}$

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!

3. Okay, so what would the answer be? I also tried just A and that is incorrect also.

4. Originally Posted by Thomas
Okay, so what would the answer be? I also tried just A and that is incorrect also.
I've been doing a number of "running" edits on your two problems. I think I've finally gotten it right on both of them now, but given all my previous errors, please check my logic to make sure it is sound!

-Dan

5. I tried using just Option B as an answer, and it say it's incorrect. Are any determined uniquely?

If none are determined uniquely, I don't see how both Option A and B are wrong...

6. Bump!

7. 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.