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

$y>14$

$4x+y<18$

The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

","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-125"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$y>14$

$4x+y<18$

The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

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

Choice A is correct. It's given that the point $(x,53)$ is a solution to the given system of inequalities in the $xy$-plane. This means that the coordinates of the point, when substituted for the variables $x$ and $y$, make both of the inequalities in the system true. Substituting $53$ for $y$ in the inequality $y>14$ yields $53>14$, which is true. Substituting $53$ for $y$ in the inequality $4x+y<18$ yields $4x+53<18$. Subtracting $53$ from both sides of this inequality yields $4x<-35$. Dividing both sides of this inequality by $4$ yields $x<-8.75$. Therefore, $x$ must be a value less than $-8.75$. Of the given choices, only $-9$ is less than $-8.75$.

Choice B is incorrect. Substituting $-5$ for $x$ and $53$ for $y$ in the inequality $4x+y<18$ yields $4(-5)+53<18$, or $33<18$, which is not true.

Choice C is incorrect. Substituting $5$ for $x$ and $53$ for $y$ in the inequality $4x+y<18$ yields $4(5)+53<18$, or $73<18$, which is not true.

Choice D is incorrect. Substituting $9$ for $x$ and $53$ for $y$ in the inequality $4x+y<18$ yields $4(9)+53<18$, or $89<18$, which is not true.

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

$y>14$

$4x+y<18$

The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

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

$-5$

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

$5$

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

$9$

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

$-9$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-125"}

$y>14$$4x+y<18$The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

$y>14$$4x+y<18$The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

$y>14$$4x+y<18$The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

$y>14$

$4x+y<18$

The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

$y>14$

$4x+y<18$

The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

$y>14$

$4x+y<18$

The point $(x,53)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?