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

$4x-9y=9y+5$

$hy=2+4x$

In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

","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-181"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$4x-9y=9y+5$

$hy=2+4x$

In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

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

Choice D is correct. A system of two linear equations in two variables, $x$ and $y$, has no solution if the lines represented by the equations in the $xy$-plane are distinct and parallel. The graphs of two lines in the $xy$-plane represented by equations in the form $Ax+By=C$, where $A,B,$ and $C$ are constants, are parallel if the coefficients for $x$ and $y$ in one equation are proportional to the corresponding coefficients in the other equation. The first equation in the given system can be written in the form $Ax+By=C$ by subtracting $9y$ from both sides of the equation to yield $4x-18y=5$. The second equation in the given system can be written in the form $Ax+By=C$ by subtracting $4x$ from both sides of the equation to yield $-4x+hy=2$. The coefficient of $x$ in this second equation, $ -4 $, is $ -1 $ times the coefficient of $x$ in the first equation, $ 4 $. For the lines to be parallel, the coefficient of $y$ in the second equation, $ h $, must also be $ -1 $ times the coefficient of $y$ in the first equation, $ -18 $. Thus, $ h=-1(-18) $, or $ h=18 $. Therefore, if the given system has no solution, the value of $h$ is $18$.

Choice A is incorrect. If the value of $h$ is $-9$, then the given system would have one solution, rather than no solution.

Choice B is incorrect. If the value of $h$ is $0$, then the given system would have one solution, rather than no solution.

Choice C is incorrect. If the value of $h$ is $9$, then the given system would have one solution, rather than no solution.

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

$4x-9y=9y+5$

$hy=2+4x$

In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

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

$ -9 $

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

$ 0 $

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

$ 9 $

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

$ 18 $

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

Choice A is incorrect. If the value of $h$ is $-9$, then the given system would have one solution, rather than no solution.

Choice B is incorrect. If the value of $h$ is $0$, then the given system would have one solution, rather than no solution.

Choice C is incorrect. If the value of $h$ is $9$, then the given system would have one solution, rather than no solution.

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

Choice A is incorrect. If the value of $h$ is $-9$, then the given system would have one solution, rather than no solution.

Choice B is incorrect. If the value of $h$ is $0$, then the given system would have one solution, rather than no solution.

Choice C is incorrect. If the value of $h$ is $9$, then the given system would have one solution, rather than no solution.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-181"}

$4x-9y=9y+5$$hy=2+4x$In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

$4x-9y=9y+5$$hy=2+4x$In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

$4x-9y=9y+5$$hy=2+4x$In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

$4x-9y=9y+5$

$hy=2+4x$

In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

$4x-9y=9y+5$

$hy=2+4x$

In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?

$4x-9y=9y+5$

$hy=2+4x$

In the given system of equations, $h$ is a constant. If the system has no solution, what is the value of $h$?