That system is the same as:



which can be written



This is a homogeneous system, which means all the
constant terms are 0.

A homogeneous system always has solution (0,0,0) and
that is the only solution it can have it the matrix
of the coefficients is not singular. 

Since we are told that x is not 0, we know that the 
matrix of coeficients is singular and therefore the 
determinant of coefficients must be 0. so we set the 
determinant of coefficients = 0.



We evaluate the determinant (I assume you know how, 
if you don't post again asking how.) We get:
 
-p + 12 = 0
     -p = -12
      p = 12

Edwin