Pulley problem - finding tensions and acceleration

[reesespieces2]

Homework Statement

I have a drawing that has two masses (unequal) hanging from a string that passes over a pulley. There is an acceleration acting on each of the forces in opposite directions. Assuming that the only given information is the masses (one is M=12 kg and the other is m=6 kg) how would I find the acceleration and the tensions on either side? (Also, the tensions are unequal)

Homework Equations

T$$^{}1$$ - Mg = -Ma
T$$_{}2$$ - mg = ma

The Attempt at a Solution

I'm not sure how to even approach this given that there are three different unknowns and only two equations.

 

[rl.bhat]

Hi reesespieces2, welcome to PF.
In a single string the tension is the same in all its segments. So T1 = T2.

 

[reesespieces2]

Thank you!