Kirchhoff's Rule and finding current with a system of equations

[MeMoses]

Homework Statement

Using Kirchhoff's rules, calculate the current in R1 with the directions indicated in the figure above. Assume that R1 = 1.00kΩ, R2 = 3.00kΩ, R3 = 5.00kΩ, E1 = 75.0V, E2 = 65.0V and E3 = 85.0V.

Homework Equations

Kirchhoff's rules

The Attempt at a Solution

Using Kirchhoff's rules I can get I2 = I1 + I3. Which so far is the only thing I'm certain is correct. Next I need two equations from the loops (left and right) and then just solve the system of equations. I don't know if I am setting these up wrong but none of my answers have been correct thus far. I got:
E1 - R1I1 - R2I2 - E2 = 0 and E2 - R2I2 - E2 - I3R3 = 0
which come out to
10 - I1 - 3(I2) = 0 and 20 - 3(I2) - 5(I3) = 0
which results with I1 = 0.869 = 0.000869A when taking into account the resistances were kiloohms. Neither of these answers are correct. Calculations shouldn;t be the problems either because I've been lazy and just plugging into wolfram alpha to solve the systems of equations. I assume I am doing something wrong with equations 2 and 3. Any help would be appreciated.

 

[gneill]

You may have slipped a sign somewhere or found the current assuming the opposite direction from that indicated. The magnitude of the value you found looks okay to me.

 

[MeMoses]

thanks, apparently all the answers were just negative

 

[MeMoses]

I thought I was done, but I have to calculate the potential between point c and f. I thought it would be E2 (65V) + I2R2 (-3.04mA*3kQ = -9.12V) = 55.9V. The parentheses there were just to clarify the values. This answer is not correct. What do I need to calculate the potential difference here, or do I just add them? If so, is there any easy way to keep track of these positives and negative which just seem to confuse things?

 

[gneill]

I thought I was done, but I have to calculate the potential between point c and f. I thought it would be E2 (65V) + I2R2 (-3.04mA*3kQ = -9.12V) = 55.9V. The parentheses there were just to clarify the values. This answer is not correct. What do I need to calculate the potential difference here, or do I just add them? If so, is there any easy way to keep track of these positives and negative which just seem to confuse things?

They seem to be trying to trip you up with sign conventions! The reality is, current is flowing from node c towards node f (they have I2 pointing upwards). So the value you obtained for I2 is negative, right?

So, proceeding from node f up through R2 there should be a voltage rise R2*|I2|. Then another rise as you go through E2. Now the question becomes, when they ask for the potential between c and f, do they want just the magnitude or are they implying a particular direction?