Let $ ABC $ be the triangle such that the equations of lines $ AB $ and $ AC $ are:
$
3y - x = 2 \quad \text{and} \quad x + y = 2,
$
respectively, and the points $ B $ and $ C $ lie on the x-axis. If $ P $ is the orthocentre of the triangle $ ABC $, then the area of the triangle $ PBC $ is equal to: