Is This the Correct Solution for Kirchhoff's Loop Problem?

[shrabastee]

Homework Statement

We are to find I1, I2 and I3 in the diagram.

Homework Equations

These are the three equations I got. I need to know if they're correct.
x=I1
y=I2
z=I3

12y-24+35x=0
35x+34z-18=0
x=y+z

The Attempt at a Solution

Values I got on solving:
I1=0.508
I2=0.511
I3=0.0029

(Note: r=1 ohm)

kindly tell me if this is correct! :)

 

[shrabastee]

Sign convention followed:

In the direction of the current=positive
Negative to positive plate=negative

 

[willem2]

Sign convention followed:

In the direction of the current=positive
Negative to positive plate=negative

The solution is correct. I almost never use the voltage/loop rule.

If you give the node at the top an unknown potential V, and the node at the bottom a potential
0, you only have to use the current rule once to get a single equation for V.