Nonlinear equations in one variable and systems of equations in two variables SAT question

Choice A is correct. It's given that the graphs of the equations in the given system of equations intersect at the point $(x,y)$. Therefore, this intersection point is a solution to the given system. The solution can be found by isolating $y$ in each equation. The given equation $8x+y=-11$ can be rewritten to isolate $y$ by subtracting $8x$ from both sides of the equation, which gives $y=-8x-11$. The given equation $2x^2=y+341$ can be rewritten to isolate $y$ by subtracting $341$ from both sides of the equation, which gives $2x^2-341=y$. With each equation solved for $y$, the value of $y$ from one equation can be substituted into the other, which gives $2x^2-341=-8x-11$. Adding $8x$ and $11$ to both sides of this equation results in $2x^2+8x-330=0$. Dividing both sides of this equation by $2$ results in $x^2+4x-165=0$. This equation can be rewritten by factoring the left-hand side, which yields $(x+15)(x-11)=0$. By the zero-product property, if $(x+15)(x-11)=0$, then $(x+15)=0$, or $(x-11)=0$. It follows that $x=-15$, or $x=11$. Since only $-15$ is given as a choice, a possible value of $x$ is $-15$. 

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.