What is the solution to this circuit problem involving Kirchoff's Laws?

[dougyunker]

Homework Statement

The circuit in the figure is composed of two batteries (ε1 = 8 V and ε2 = 5 V) and four resistors (R1 = 110 Ω, R2 = 40 Ω, R3 = 50 Ω, and R4 = 50 Ω) as shown.

Image: See Attachment
OR: https://smart.physics.illinois.edu/images/phys102/Homework/03/cir06.gif

Homework Equations

I1=I4=I2+I3
E1-I1R1-I3R3-I4R4=0
E1-I1R1-I2R2-E2-I4R4=0

The Attempt at a Solution

First Equation: 8-110(I1)-50(I3)-50(I4)=0
Sub I4=I1 -> 8-160(I1)-50(I3)=0
Second Equation: 8-110(I1)-40(I2)-5-50(I4)=0
Sub I4=I1 -> 3-160(I1)-40(I2)=0
Sub I2=I1-I3 -> 160(I1)+40(I1)-40(I3)=3

Compare two equations:

160(I1)+50(I3)=8
200(I1)-40(I3)=3

The answers I got for I1 and I3 arent the correct answers. I've been working on this problem for awhile and am getting frustrated. Any help would be appreciated. Thanks, Doug

 

[dougyunker]

bump please