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

Which of the following systems of linear equations has no solution?

","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-171"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

Which of the following systems of linear equations has no solution?

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

Choice C is correct. A system of two linear equations in two variables, $x$ and $y$, has no solution if the graphs of 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 slope-intercept form, $y=mx+b$, where $m$ and $b$ are constants, are parallel if their slopes, $m$, are the same and are distinct if their $y$-coordinates of the $y$-intercepts, $b$, are different. In the equations $y=16x+3$ and $y=16x+19$, the values of $m$ are each $16$, and the values of $b$ are $3$ and $19$, respectively. Since the slopes of these lines are the same, and the $y$-coordinates of the $y$-intercepts are different, it follows that the system of linear equations in choice C has no solution.

Choice A is incorrect. The lines represented by the equations in this system are a vertical line and a horizontal line. Therefore, this system has a solution, $(3,5)$, rather than no solution.

Choice B is incorrect. The two lines represented by these equations have different slopes and the same $y$-coordinate of the $y$-intercept. Therefore, this system has a solution, $(0,6)$, rather than no solution.

Choice D is incorrect. The two lines represented by these equations are a horizontal line and a line with a slope of $5$ that have the same $y$-coordinate of the $y$-intercept. Therefore, this system has a solution, $(0,5)$, rather than no solution.

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Which of the following systems of linear equations has no solution?

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

$x=3$

$y=5$

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

$y=6x+6$

$y=5x+6$

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

$y=5$

$y=5x+5$

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

$y=16x+3$

$y=16x+19$

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

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

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