Assuming the two equations are independent (I didn't check) you can solve for two of the unknowns in terms of the other, say, solving for x and y in terms of z. Letting z= t, we have the parametric equations, x= x(t), y= y(t), z= t. Since that depends on one parameter, it describes a "one dimensional" geometric object. Since the equations are linear, It is a straight line.