Finding currents I1, I2, I3 using Kirchhoff's laws

[klandestine]

I have attached a picture of a circuit. I am trying to find the values of I₁, I₂, and I₃. What I have come up with so far, using Kirchhoff's Voltage and Junction Laws is:
I₂=I₁+I₃
for the left loop:
9V - (5 ohms)I₁ -4V - (10 ohms)I₂ = 0
which simplifies to:
1V - (1 ohm)I₁ - (2 ohms)I₂ = 0
for the right loop:
14V - (10 ohms)I₃ -4V - (10 ohms)I₂ = 0
which simplifies to:
1V - (1 ohm)I₃ - (1 ohm)I₂ = 0
I am pretty certain that I have these correct, but I can't seem to solve my system of equations--whenever I try to add or subtract the equations, several terms cancel, leaving me with a current equaling zero.
I would really appreciate some help. Thank you. :!)

 

[Fermat]

Answered in "introductory Physics" forum.