2x + 3y = -5
3x - 2y = 12

The answer is not (7,0).  You must have looked at the
answer to the wrong problem.

We look at the two coefficients of y.  They are +3 in the first
equation and -2 in the second. The least common multiple of |+3|
and |-2| is 6.  

So if we multiply both sides of the first equation by 2 and 
both sides of the second equation by 3, we get

 4x + 6y = -10
 9x - 6y =  36

Now when we add equals to equals, the +6y in the first will cancel
with the -6y in the second:

 4x + 6y = -10
 9x - 6y =  36 
--------------
13x      =  26
  x      =  2

Then we substitute that in either or the original equations:

  2x + 3y = -5
2(2) + 3y = -5
   4 + 3y = -5
       3y = -9
        y = -3

So the answer is (2,-3).

Checking the first equation:

     2x + 3y = -5
2(2) + 3(-3) = -5
       4 - 9 = -5 
          -5 = -5

Checking the second equation:

     3x - 2y = 12
3(2) - 2(-3) = 12
       6 + 6 = 12
          12 = 12

So the answer is (2,-3), not (7,0).

Edwin