sat-dog

Choice A is correct. It’s given that the point $\left(x,53\right)$ is a solution to the given system of inequalities in the xy-plane. This means that the coordinates of the point, when substituted for the variables $x$ and $y$, make both of the inequalities in the system true. Substituting $53$ for $y$ in the inequality $y>14$ yields $53>14$, which is true. Substituting $53$ for $y$ in the inequality $4x+y<18$ yields $4x+53<18$. Subtracting $53$ from both sides of this inequality yields $4x<-35$. Dividing both sides of this inequality by $4$ yields $x<-8.75$. Therefore, $x$ must be a value less than $-8.75$. Of the given choices, only $-9$ is less than $-8.75$.

Choice B is incorrect. Substituting $-5$ for $x$ and $53$ for $y$ in the inequality $4x+y<18$ yields $4\left(-5\right)+53<18$, or $33<18$, which is not true.

Choice C is incorrect. Substituting $5$ for $x$ and $53$ for $y$ in the inequality $4x+y<18$ yields $4\left(5\right)+53<18$, or $73<18$, which is not true.

Choice D is incorrect. Substituting $9$ for $x$ and $53$ for $y$ in the inequality $4x+y<18$ yields $4\left(9\right)+53<18$, or $89<18$, which is not true.