Two Loops, Two Batteries: Find the Currents

[JP4Fun]

Homework Statement

Question: Find the current in the circuit shown.
http://i1307.photobucket.com/albums/s599/JustOn4Fun/PhysicsFigure_zps39d4c66d.png

Homework Equations

Not sure if equations are necessary since it's a question testing the use of the following rules:
Junction Rule
The Loop Rule

The Attempt at a Solution

At Junction A: I1-I2-I3=0
At Junction B:-I1+I2+I3=0
Loop 1:15V-I3R-I1R=0
Loop 2:-9V-I2R+I3R=0

I1=I2+I3

15V-100I3-100I1=0
15/100=I3+I1=.15

-9V-100I2+I3=0
I3-I2=9/100=.09

(I3+I1)-(I3-I2)=.06
I1+I2=.06

I think I'm having a brain fart or something because it feels like I'm just messing with the problem but not seeing something that's right under my nose. Thank you for the help!

 

[ehild]

Cancel one of the currents from the equations. For example, substitute I2+I3 for I1 into the first loop equation.

ehild

 

[JP4Fun]

I tried what you said and got the following:
15V-I3R-(I2+I3)R=0
and when the I3R cancels out, I'm left with 15V-I2R=0 giving me I2=.15

The answers are: I1=0.070A, I2=-0.010A, and I3=0.080A

What am I doing wrong?

 

[ehild]

I tried what you said and got the following:
15V-I3R-(I2+I3)R=0
and when the I3R cancels out?, I'm left with 15V-I2R=0 giving me I2=.15

The answers are: I1=0.070A, I2=-0.010A, and I3=0.080A

What am I doing wrong?

I3 does not cancel out.

ehild

 

[JP4Fun]

I3 does not cancel out.

ehild

I tried what you said and got the following:
15V-I3R-(I2+I3)R=0
and when the I3R cancels out, I'm left with 15V-I2R=0 giving me I2=.15

The answers are: I1=0.070A, I2=-0.010A, and I3=0.080A

What am I doing wrong?

Ah, yeah bad mistake. I got...
15V-2I3R-I2R=0
15V=2I3R-I2R
Unfortunately, I'm not seeing it haha

 

[ehild]

Now you have two equation with two unknowns.
15V=2I3R-I2R
-9V-I2R+I3R=0

Isolate I2 from one of them and substitute into the other one.

ehild

 

[ehild]

Ah, yeah bad mistake. I got...
15V-2I3R-I2R=0
[STRIKE]15V=2I3R-I2R[/STRIKE]
Unfortunately, I'm not seeing it haha

A sign error again.
Now you have two equation with two unknowns.
15V-2I3R-I2R=0
-9V-I2R+I3R=0

Isolate I2 from one of them and substitute into the other one.

ehild

 

[JP4Fun]

Ah, I got it now. Thank you very much for being patient with me.

 

[ehild]

You are welcome

ehild