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

$y\\leq 3x+1$

$x-y>1$

Which of the following ordered pairs $(x,y)$ satisfies 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-233"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$y\\leq 3x+1$

$x-y>1$

Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

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

Choice D is correct. Any point $(x, y)$ that is a solution to the given system of inequalities must satisfy both inequalities in the system. The second inequality in the system can be rewritten as $x>y+1$. Of the given answer choices, only choice D satisfies this inequality, because inequality $2>-1+1$ is a true statement. The point $(2,-1)$ also satisfies the first inequality.

Alternate approach: Substituting $(2,-1)$ into the first inequality gives $-1\\leq 3(2)+1$, or $-1\\leq 7$, which is a true statement. Substituting $(2,-1)$ into the second inequality gives $2-(-1)>1$, or $3>1$, which is a true statement. Therefore, since $(2,-1)$ satisfies both inequalities, it is a solution to the system.

Choice A is incorrect because substituting $-2$ for $x$ and $-1$ for $y$ in the first inequality gives $-1\\leq 3(-2)+1$, or $-1\\leq-5$, which is false. Choice B is incorrect because substituting $-1$ for $x$ and $3$ for $y$ in the first inequality gives $3\\leq 3(-1)+1$, or $3\\leq-2$, which is false. Choice C is incorrect because substituting 1 for $x$ and 5 for $y$ in the first inequality gives $5\\leq 3(1)+1$, or $5\\leq 4$, which is false.

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

$y\\leq 3x+1$

$x-y>1$

Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

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

$(-2,-1)$

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

$(-1,3)$

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

$(1,5)$

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

$(2,-1)$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-233"}

$y\\leq 3x+1$$x-y>1$Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

$y\\leq 3x+1$$x-y>1$Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

$y\\leq 3x+1$$x-y>1$Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

$y\\leq 3x+1$

$x-y>1$

Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

$y\\leq 3x+1$

$x-y>1$

Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

$y\\leq 3x+1$

$x-y>1$

Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

$y\leq 3x+1$$x-y>1$Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?

$y\leq 3x+1$

$x-y>1$

Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities above?