y ≤ x + 7 y ≥ - 2 x - 1 Which point x ,

Choice D is correct. A point $\left(x,y\right)$ is a solution to a system of inequalities in the xy-plane if substituting the x-coordinate and the y-coordinate of the point for $x$ and $y$, respectively, in each inequality makes both of the inequalities true. Substituting the x-coordinate and the y-coordinate of choice D, $14$ and $0$, for $x$ and $y$, respectively, in the first inequality in the given system, $ydx+7$, yields $0d14+7$, or $0d21$, which is true. Substituting $14$ for $x$ and $0$ for $y$ in the second inequality in the given system, $ye-2x-1$, yields $0e-2\left(14\right)-1$, or $0e-29$, which is true. Therefore, the point $\left(14,0\right)$ is a solution to the given system of inequalities in the xy-plane.

Choice A is incorrect. Substituting $-14$ for $x$ and $0$ for $y$ in the inequality $ydx+7$ yields $0d-14+7$, or $0d-7$, which is not true.

Choice B is incorrect. Substituting $0$ for $x$ and $-14$ for $y$ in the inequality $ye-2x-1$ yields $-14e-2\left(0\right)-1$, or $-14e-1$, which is not true.

Choice C is incorrect. Substituting $0$ for $x$ and $14$ for $y$ in the inequality $ydx+7$ yields $14d0+7$, or $14d7$, which is not true.