OK, the determinamt is equal to zero (I should have checked). This means that either there's no solution or an infinite number of solutions. So my suggestion is no good after all.
In fact, since x = 3y + 8z from the first equation, the second and third equations become:
y + 2z = 0 and y + 2z = 13/2.
Therefore the equations are INconsistent and there is no solution to be found.