I just found that the question was looking for me to show a 0=0 case to mean they are linearly independent then express x,y,z in terms of a parameter
you're welcome,
well to show that system of equations are consistent you can do it with that property that D=D_x=D_y=D_z =0 and that at least one sub determinant of D is different from zero ... that will tell you that your equations are consistent, this is more a theoretical thing
but best thing is to consult with you teacher about this or at least someone whom have similar type of education (and same country lol) good luck on the exams