{"@context":"https://schema.org/","@type":"Quiz","name":"

$8x+y=-11$

$2x^{2}=y+341$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-98"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$8x+y=-11$

$2x^{2}=y+341$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

","comment":{"@type":"Comment","text":"

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.

"},"encodingFormat":"text/markdown","text":"

$8x+y=-11$

$2x^{2}=y+341$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

","suggestedAnswer":[{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$-11$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$2$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$8$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$-15$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-98"}

$8x+y=-11$$2x^{2}=y+341$The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

$8x+y=-11$$2x^{2}=y+341$The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

$8x+y=-11$$2x^{2}=y+341$The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

$8x+y=-11$

$2x^{2}=y+341$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

$8x+y=-11$

$2x^{2}=y+341$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?

$8x+y=-11$

$2x^{2}=y+341$

The graphs of the equations in the given system of equations intersect at the point $(x,y)$ in the $xy$-plane. What is a possible value of $x$?