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

$y\\leq x$

$y\\leq-x$

Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

","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-35"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$y\\leq x$

$y\\leq-x$

Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

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

Choice D is correct. The solution to the given system of inequalities is the set of all ordered pairs $(x,y)$ that satisfy both inequalities in the system. For an ordered pair to satisfy the inequality $y\\leq x$, the value of the ordered pair's $y$-coordinate must be less than or equal to the value of the ordered pair's $x$-coordinate. This is true of the ordered pair $(0,-1)$, because $-1\\leq 0$. To satisfy the inequality $y\\leq-x$, the value of the ordered pair's $y$-coordinate must be less than or equal to the value of the additive inverse of the ordered pair's $x$-coordinate. This is also true of the ordered pair $(0,-1)$. Because $0$ is its own additive inverse, $-1\\leq-(0)$ is the same as $-1\\leq0$. Therefore, the ordered pair $(0,-1)$ is a solution to the given system of inequalities.

Choice A is incorrect. This ordered pair satisfies only the inequality $y \\leq x$ in the given system, not both inequalities. Choice B is incorrect. This ordered pair satisfies only the inequality $y \\leq -x$ in the system, but not both inequalities. Choice C is incorrect. This ordered pair satisfies neither inequality.

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

$y\\leq x$

$y\\leq-x$

Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$(1,0)$

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

$(-1,0)$

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

$(0,1)$

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

$(0,-1)$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-35"}

$y\\leq x$$y\\leq-x$Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

$y\\leq x$$y\\leq-x$Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

$y\\leq x$$y\\leq-x$Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

$y\\leq x$

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Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

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$y\\leq-x$

Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

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Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?

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$y\leq x$

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Which of the following ordered pairs $(x,y)$ is a solution to the system of inequalities above?