Given equations,
4x - y = 19----------------------@1
x - y = 4------------------------@2
x + 2y = -11 --------------------@3
solving 1st and 2nd, we'll get
$x_{1} = 5, y_{1} = 1$
solving 2nd and 3rd, we'll get
$x_{2} = -1, y_{2} = -5$
solving 1st and 3rd, we'll get
$x_{3} = 3, y_{3} = -7$
The 3 vertices of the triangle (5,1), (-1,-5) and (3,-7)
Centroid of the triangle,
$(O_{x}, O_{y}) = \left ( \frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3} \right ) = \left ( \frac{5 - 1 + 3}{3}, \frac{1 - 5 -7}{3}\right ) = \left ( \frac{7}{3},\frac{-11}{3} \right )$
Option D.