MHB Linear Applications: Electrical Networks

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The discussion revolves around solving a circuit problem to determine branch currents using assigned variables and equations. The user created three equations based on their circuit analysis but found a discrepancy between their calculated results and the book's solutions. The user’s derived currents are I1=35/13, I2=20/13, and I3=15/13, while the book states I1=5/7, I2=20/7, and I3=15/7. Another participant suggests that the user's equations are correct and that the book's solutions likely pertain to a different problem with different resistor values. The conclusion indicates that the initial setup of equations is not the issue, but rather the book's provided answers.
Pull and Twist
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So I am having difficulty with the following problem;

Determine the currents in the various branches.

View attachment 5184

So I went ahead and assigned I names to the various branches and drew in flow directions to help me visualize the problem better.

From there I created the following three equations;

I1=I2+I3
2I1+3I2=10
2I1+4I3=10

Which I then put in a matrix and was able to reduce for the following solutions;

I1=35/13
I2=20/13
I3=15/13

The problem is that the book states that I should be getting;

I1=5/7
I2=20/7
I3=15/7

Where am I going wrong in setting up my equations? I know I'm not messing up going to RREF form cause my calculator is giving me the same answer. I figure I must be screwing up the initial equations.
 

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Hi PullandTwist,

I believe your equations and solution are fine.
The stated book solution is wrong.
It looks as if it belongs to a similar problem with different resistors.
For instance with resistors $2\ \Omega, 2\ \Omega, 6\ \Omega$ and voltage $10\ \textrm{V}$.
 
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