Question

$$P + 1 / q = 1 , q + 1 / r = 1$$

Solve for P, q, r (complex solution)

$r=-\frac{1}{q-1}$
$P=\frac{q-1}{q}$
$q\in \mathrm{C}\setminus 1,0$

Solve for P, q, r

$r=-\frac{1}{q-1}$
$P=\frac{q-1}{q}$
$q\in \mathrm{R}\setminus 1,0$