I assume that there is a missing z in each equation.
If that is the case, the solution using matrices and determinants is x=255/119, y=67/119, z=-12/119.
CHECK
Plug these values into the original equations:
(255+134+444)/119=833/119=7; (255+67-84)/119=238/119=2; (510-67-324)/119=119/119=1. So all equations are satisfied. The solution is correct.