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

The point $(8,2)$ in the xy-plane is a solution to which of the following systems of inequalities?

","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-algebra-multiple-choice-question-6"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

The point $(8,2)$ in the xy-plane is a solution to which of the following systems of inequalities?

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

Choice A is correct. The given point, $(8,2)$, is located in the first quadrant in the $xy$-plane. The system of inequalities in choice A represents all the points in the first quadrant in the $xy$-plane. Therefore, $(8,2)$ is a solution to the system of inequalities in choice A.

Alternate approach: Substituting $8$ for $x$ in the first inequality in choice A, $x>0$, yields $8>0$, which is true. Substituting $2$ for $y$ in the second inequality in choice A, $y>0$, yields $2>0$, which is true. Since the coordinates of the point $(8,2)$ make the inequalities $x>0$ and $y>0$ true, the point $(8,2)$ is a solution to the system of inequalities consisting of $x>0$ and $y>0$.

Choice B is incorrect. This system of inequalities represents all the points in the fourth quadrant, not the first quadrant, in the $xy$-plane.

Choice C is incorrect. This system of inequalities represents all the points in the second quadrant, not the first quadrant, in the $xy$-plane.

Choice D is incorrect. This system of inequalities represents all the points in the third quadrant, not the first quadrant, in the $xy$-plane.

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

The point $(8,2)$ in the xy-plane is a solution to which of the following systems of inequalities?

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

$x>0 \\\\ y<0$

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

$x<0 \\\\ y>0$

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

$x<0 \\\\ y<0$

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

$x>0 \\\\ y>0$

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

Choice C is incorrect. This system of inequalities represents all the points in the second quadrant, not the first quadrant, in the $xy$-plane.

Choice D is incorrect. This system of inequalities represents all the points in the third quadrant, not the first quadrant, in the $xy$-plane.

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

Choice C is incorrect. This system of inequalities represents all the points in the second quadrant, not the first quadrant, in the $xy$-plane.

Choice D is incorrect. This system of inequalities represents all the points in the third quadrant, not the first quadrant, in the $xy$-plane.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-6"}