Are My Equations Correct for Kirchoff's Rules?

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SUMMARY

The discussion centers on the application of Kirchhoff's Rules in circuit analysis, specifically addressing the equations derived for loop and node analysis. The initial equations presented were found to be incorrect, particularly the loop 1 equation, which was simplified incorrectly. After adjusting the node equation to I1 = I2 + I3, the correct current values were obtained, resolving the discrepancies in the calculations. The final conclusion emphasizes the importance of correctly referencing loop currents rather than using the problem's current designations.

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My loop 1 equation is I1R1 + I2R2 + E1 = 0
simplified to: 4I1 + 2I2 + 28 = 0
Loop 2: I3R3 - E2 - I2R2 = 0
simplified to: 1I3 - 7V - 2I2 = 0

And my node 1 equation is: 0 = I1 + I2 + I3

So doing algebra.. I get my I1 to equal 7.. which doesn't match with the -5A for I1 as given in the problem.

Are my equations wrong? Or is my algebra wrong?
 

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Loop 1 equation is wrong. No need to go further till that's fixed. I think you are trying to use the I references from the problem. Don't. Use only Iloop1 and Iloop2.
 
Okay well I changed my node equation to I1 = I2 + I3 and got the right answer in the end.
 

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