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 -10 from the first equation, Mr F says: An embarrassing correction in red. So what follows is wrong.
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.
Therefore the second and third equations become y + 2z = 3 and y + 2z = 3. Therefore there are an infinite number of solutions (the one given by CB is once such). These solutions can be expressed in parametric form. The system is consistent.