9x + 3y = 6
    6x + 2y = 5

To eliminate y.

1. Get the least common multiple of the coefficients of 
   y which are 3 and 2.  That's 6
2. We need to make one the coefficient of y in one of 
   the equations to become 6 and the coefficient of y in 
   the other equation other become -6, so the terms in y 
   will cancel when we add the equations term by term.
   We multiply the first equation through by 2, getting
    18x + 6y =  12

   We multiply the second equation through by -3, getting
   -18x - 6y = -15   

3. Now we have this system, and we add them term by term:

    18x + 6y =  12
   -18x - 6y = -15
   ———————————————
     0  +  0 =  -3
           0 =  -3

4.  All the letters cancel out leaving only numbers.  When such
    an equation is true the system is dependent and has infinitely
    many solutions.  But when it is false, like this case 0 = -3, 
    the system is INCONSISTENT and there is no solution. 

5.  The graphs of the two equations are parallel and therefore they
    do not intersect to form a solution.  Here are their graphs.
    The graph of the first equation is red and the graph of the second
    equation is green: 
    
    
Edwin