System of Equations , Finding value of coefficient so equations are inconsistent 

Question; Calculate a value for the coefficient $'a'$ of $x$ so that the solutions to the three equations are inconsistent. Demonstrate the resulting system of equations are then inconsistent:
    $$ x+2y+2z=6$$
    $$ x-y+z=-4$$
    $$  ax+y-9z=-1$$
Cannot use matrix/matrics



What I have attempted:
Using the first 2 equations to eliminate $z$ 
$$ x+2y+2z=-6$$
$$ x-y+z=-4$$
Multiplying the second by $2$
$$ x+2y+2z=6$$
$$ 2x-2y+2z=-8$$
Subtracting both to get 
$$ -x + 4y = 14 $$
$$ y = \frac{14}{4} + \frac{x}{4} $$
Again using the first 2 equations to eliminate y
$$ x+2y+2z=-6$$
$$ x-y+z=-4$$
Multiplying the second by $-2$
$$ x + 2y + 2z = -6 $$
$$ -2x + 2y - 2z = 8 $$
Subtracting
$$ 3x +  4z = -14 $$
$$ z = \frac{-14}{4} - \frac{3x}{4} $$
Subbing both $z$ and $y$ into $ax+y-9z=-1$
$$ ax + \frac{14}{4} + \frac{x}{4} -9(\frac{-14}{4} - \frac{3x}{4}) = -1 $$
$$ax + \frac{14}{4} + \frac{x}{4} + \frac{63}{2} + \frac{27x}{4} = -1  $$ 
$$ ax  + 7x = -36 $$
$$ x(a+7) = -36 $$
Now I am stuck, how do I find the value of a?

Here is a computer doing basic algebra. It is tedious to do it by hand.

Leting $a= \frac{-28}{4}$ will reduce the system to $0x+0y+0za=1$ and $0 \neq 1$

