Which equation below is the correct equation for Loop 1?

Yellow: -V₂ + I₁R₁ - I₂R₂ = 0                                     

Pink: V₂ + I₁R₁ - I₂R₂ = 0

Green: -V₂ - I₁R₁ + I₂R₂ = 0                                        

Blue: V₂ + I₁R₁ + I₂R₂ = 0

Purple: None of these.

Answer: Yellow, -V₂ + I₁R₁ - I₂R₂ = 0. As we move aroung loop 1, we go through the battery from the (+) to the (-) side, a voltage drop so the voltage change is -V₂. Then we go through R₁ from the low V side to the high V side (since we are moving against the current flow I₁): a voltage rise so the change is +I₁R₁. Finally, we go through R₂, in the same direction as the current I₂, so we have a voltage drop and a change of -I₂R₂. The total change as we moved around the loop must be zero, since we finished at the point where we started.