Multiply equation 1 by -3 and add it to equation 2 to get

Multiply eqaution 1 by -4 and add it to equation 3 to get

Now multiply the first of these equations by -1 and add it to the other to get

Now we factor the left hand side to get

Now lets check some values of a

Case I: a=4

we get 0=0 so the system is consistant dependant (has an infinite number of solutions.)

Case II: a=-4

We get 0=-8 So the system in inconsistant(has no solutions)

Case III:

we get

The system has exactly one solution and it is given above.

So the system is consistant independant.

I hope this clear it up.

Note this could have been done with a matrix and putting the matrix into eschelon form.