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

$y\\leq x+7$

$y\\geq-2x-1$

Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

","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-46"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$y\\leq x+7$

$y\\geq-2x-1$

Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

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

Choice D is correct. A point $(\\bm{x},\\bm{y})$ is a solution to a system of inequalities in the $xy$-plane if substituting the $x$-coordinate and the $y$-coordinate of the point for $x$ and $y$, respectively, in each inequality makes both of the inequalities true. Substituting the $x$-coordinate and the $y$-coordinate of choice D, 14 and 0, for $x$ and $y$, respectively, in the first inequality in the given system, $y\\leq x+7$, yields $0\\leq 14+7$, or $0\\leq 21$, which is true. Substituting 14 for $x$ and 0 for $y$ in the second inequality in the given system, $y\\geq-2x-1$, yields $0\\geq-2(14)-1$, or $0\\geq-29$, which is true. Therefore, the point $(14,0)$ is a solution to the given system of inequalities in the $xy$-plane.

Choice A is incorrect. Substituting $-14$ for $x$ and 0 for $y$ in the inequality $y\\leq x+7$ yields $0\\leq-14+7$, or $0\\leq-7$, which is not true.

Choice B is incorrect. Substituting 0 for $x$ and $-14$ for $y$ in the inequality $y\\geq-2x-1$ yields $-14\\geq-2(0)-1$, or $-14\\geq-1$, which is not true.

Choice C is incorrect. Substituting 0 for $x$ and 14 for $y$ in the inequality $y\\leq x+7$ yields $14\\leq 0+7$, or $14\\leq 7$, which is not true.

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

$y\\leq x+7$

$y\\geq-2x-1$

Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

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

$(-14,0)$

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

$(0,-14)$

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

$(0,14)$

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

$(14,0)$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-46"}

$y\\leq x+7$$y\\geq-2x-1$Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y\\leq x+7$$y\\geq-2x-1$Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y\\leq x+7$$y\\geq-2x-1$Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y\\leq x+7$

$y\\geq-2x-1$

Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y\\leq x+7$

$y\\geq-2x-1$

Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y\\leq x+7$

$y\\geq-2x-1$

Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y\leq x+7$$y\geq-2x-1$Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y\leq x+7$

$y\geq-2x-1$

Which point $(x,y)$ is a solution to the given system of inequalities in the $xy$-plane?