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

$x^{2}=6x+y$
$y=-6x+36$

A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

","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-136"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$x^{2}=6x+y$
$y=-6x+36$

A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

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

Choice A is correct. Solutions to the given system of equations are ordered pairs $(x,y)$ that satisfy both equations in the system. Adding the left-hand and right-hand sides of the equations in the system yields $x^{2}+y=6x+y-6x+36$, or $x^{2}+y=y+36$. Subtracting $y$ from both sides of this equation yields $x^{2}=36$. Taking the square root of both sides of this equation yields $x=6$ and $x=-6$. Therefore, there are two solutions to this system of equations, one with an x-coordinate of $6$ and the other with an x-coordinate of $-6$. Substituting $6$ for $x$ in the second equation yields $ y=-6(6)+36$, or $y=0$; therefore, one solution is $ (6,0)$. Similarly, substituting $ -6$ for $x$ in the second equation yields $ y=-6(-6)+36$, or $y=72$; therefore, the other solution is $ (-6,72)$. It follows then that if $ (x,y)$ is a solution to the system, then possible values of $ xy$ are $ (6)(0)=0$ and $ (-6)(72)=-432$. Only $0$ is among the given choices.

Choice B is incorrect. This is the x-coordinate of one of the solutions, $ (6,0)$. Choice C is incorrect and may result from conceptual or computational errors. Choice D is incorrect. This is the square of the x-coordinate of one of the solutions, $ (6,0)$.

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

$x^{2}=6x+y$
$y=-6x+36$

A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

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

$6$

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

$12$

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

$36$

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

$0$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-136"}

$x^{2}=6x+y$ $y=-6x+36$A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

$x^{2}=6x+y$ $y=-6x+36$A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

$x^{2}=6x+y$ $y=-6x+36$A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

$x^{2}=6x+y$
$y=-6x+36$

A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

$x^{2}=6x+y$
$y=-6x+36$

A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?

$x^{2}=6x+y$
$y=-6x+36$

A solution to the given system of equations is $(x,y)$. Which of the following is a possible value of $xy$?