Identify the system as consistent or inconsistent and dependent or independent 6x-3y=18 -2x-y=-6

Try this:

Mult. the 2nd eqn by 3:

6x-3y=18
-2x-y=-6   =>         -6x - 3y = -18

To this result
add the 1st eqn:    6x  -3y = 18
                           
Adding these
eqns together:      0 = -6y = 0.  This can be solved for y:  y = 0.  Then 
                                                  -2x - 0 = -6, and x = 3.

This system has the solution x=3, y=0:  (3,0).  Check it!

Thus, we dub this system of linear equations "consistent."