Javier, please always include the source code in order to be able to understand what the issue is.
I tried with this and it seems to work:
Solve[
{(o - x) (n - x - y - z) == (a - x - y) (b - x - z),
(p - y) (n - x - y - z) == (a - x - y) (c - y - z),
(q - z) (n - x - y - z) == (b - x - z) (c - y - z)},
{x, y, z}]
