Answer
$v1 = 12V$ , $v2 = 2V$
Work Step by Step
Apply KVL by summing the voltage drops, clockwise around the two loops
Starting with the left loop
$ΣV = -5 + 3 + v2 = 0$
Solving for v2
$v2 = 2V$
Now apply to the right loop and use v2 for the middle resistor
$ΣV = -2 - 10 + v1 = 0$
$v1=12V$
