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

$y>2x-1$

$2x>5$

Which of the following consists of the $y$-coordinates of all the points that satisfy 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-173"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$y>2x-1$

$2x>5$

Which of the following consists of the $y$-coordinates of all the points that satisfy the system of inequalities above?

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

Choice B is correct. Subtracting the same number from each side of an inequality gives an equivalent inequality. Hence, subtracting 1 from each side of the inequality $2x>5$ gives $2x-1>4$. So the given system of inequalities is equivalent to the system of inequalities $y>2x-1$ and $2x-1>4$, which can be rewritten as $y>2x-1>4$. Using the transitive property of inequalities, it follows that $y>4$.

Choice A is incorrect because there are points with a $y$-coordinate less than 6 that satisfy the given system of inequalities. For example, $(3,5.5)$ satisfies both inequalities. Choice C is incorrect. This may result from solving the inequality $2x>5$ for $x$, then replacing $x$ with $y$. Choice D is incorrect because this inequality allows $y$-values that are not the $y$-coordinate of any point that satisfies both inequalities. For example, $y=2$ is contained in the set $y>\\dfrac{3}{2}$; however, if 2 is substituted into the first inequality for $y$, the result is $x<\\dfrac{3}{2}$. This cannot be true because the second inequality gives $x>\\dfrac{5}{2}$.

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

$y>2x-1$

$2x>5$

Which of the following consists of the $y$-coordinates of all the points that satisfy the system of inequalities above?

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

$y>6$

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

$y>\\dfrac{5}{2}$

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

$y>\\dfrac{3}{2}$

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

$y>4$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-173"}