Finding Current Through Resistors in Figure

[khoaz]

Determine the magnitude of the current through all the resistors shown in the figure

The batteries have emfs of E1 = 9.00V and E2 = 12.00V and the resistors have values of R1 = 15.8Ohm , R2 = 22.3Ohm, and R3 = 34.3Ohm.maybe I am just setting up my equations wrong?
E2 - I3R3 - I2R2 = 0
E1 - I1R1 - I2R2 = 0
I2 = I1 + I3

so i used one equation to solve for the other unknowns, and plugged in the i2 = i1 + i3 equation in the beginning. than used that equation to solve for the final one. maybe my algebra got screwed up along the way or something. it takes like a page working through the problem only to see that you didnt get it.so solving for I1 i tried
E2 -I1R1 - R2(E2 + I1R3)/(R3 + R2) = 0
which turned out to be .515 AI2:
E2 - R3(I2 + [I2R2/R1]) - I2R2 = 0
which turned out to be .199 AI3:
E1 - I3R3 - I3R2 - R2(E2 - I3R2)/(R1 + R2) = 0
which turned out to be .2299 A
sadly they're all wrong.

 

[Astronuc]

E2 - I3R3 - I2R2 = 0
E1 - I1R1 - I2R2 = 0
I2 = I1 + I3

are correct. One must be careful with the substitutions and signs.

E2 - I3R3 - I2R2 = 0
E1 - I1R1 - I2R2 = 0

and one can use I2 = I1 + I3 to change I3 into I2 - I1.

With E2 - (I2 - I1) R3 - I2 R2 = 0
and E1 - I1 R1 - I2 R2 = 0,

one has two equations and two unknowns I1 and I2, and then find I3.

 

[ogb p]

I would first check my calculations to ensure that I have used the correct equations and values for the resistors and emfs. I would also double check my algebra to make sure there are no errors. Additionally, I would consider the direction of the current flow and whether it aligns with the assumed direction in the equations. If all of these factors check out, then I would suggest using a circuit simulator or conducting an actual experiment to verify the values of the current through each resistor. It is possible that there may be additional factors at play, such as internal resistance of the batteries or temperature effects, that may affect the final values. It is important to thoroughly analyze and troubleshoot any discrepancies in order to ensure accurate results.