If centroid of the points $(3,5)$, $(6,y)$ and $(-3,4)$ is $(x,y)$, then find the values of $x$ and $y$.

1. The coordinates of the centroid of a triangle with vertices $({幕}_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ are given by:
$$x=\frac{x_1+x_2+x_3}{3},y=\frac{y_1+y_2+y_3}{3}$$
Substitute the given vertices $(3,5)$, $(6,y)$, and $(-3,4)$ into the formula for $x$:
$$x=\frac{3+6+(-3)}{3}=\frac{6}{3}=2$$
Substitute the vertices into the formula for $y$:
$$y=\frac{5+y+4}{3}$$
$$3y=9+y$$
$$2y=9⟹y=\frac{9}{2}$$
Thus, $x=2$ and $y=\frac{9}{2}$.