How to solve 4 variables I received the below puzzle today (via whatsapp):



We tried to solve this, but we can't solve.
We think that this puzzle is wrong.
Can this be solved? Or is this a wrong puzzle?
 A: You can write the unknowns like this:   
$a$ ;       $a-9$
$12-a$ ;    $-2-a$ 
This helps you keep the number of unknowns minimal (just $a$).   
Now the horizontal ones are satisfied and so is the 1st vertical.
Then (from the 2nd vertical) you get  $(a-9) + (-2-a) = 2$ which can never be true.
So this puzzle has no solution indeed.   
A: Okay
So A - B = 9; A = 9 + B
C - D = 14; C = 14 + D
A + C = 12; (9+B) + (14+D) = 12; B+D = -11
B + D = 2
So B + D-11 = 2.  There are no solutions.
Unless there is some other trick.  Do you know where this puzzle came from?
A: Change the minus signs to plus signs. Then, if/when we get a solution, we can convert our entries back to fit the original problem.
Now if we add the numbers on the right, we have the sum of all four entries: $$ (a + b) + (c + d) = 9 + 14 = 23$$
Similarly, if we add the numbers along the bottom, we have a different expression of the sum of the four entries: $$(a + c) + (b + d) = 12 + 2 = 14$$
Obviously, $23 \neq 14$, and the puzzle is ill-posed. 
A: Considering the top two squares as $a$ and $b$, the bottom squares as $c$ and $d$, then
$$a = 4.5 \\
b = -4.5 \\
c = 7.5 \\
d = 6.5$$
