{"@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-168"}],"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 A 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 $y=6x+3$ and $y=6x+9$, the values of $m$ are each $6$, and the values of $b$ are $3$ and $9$, 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 A has no solution.

Choice B is incorrect. The two lines represented by these equations are a horizontal line and a line with a slope of $10$ that have the same $y$-coordinate of the $y$-intercept. Therefore, this system has a solution, $(0,10)$, rather than no solution.

Choice C 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, $(0,14)$, rather than no solution.

Choice D is incorrect. The two lines represented by these equations are a vertical line and a horizontal line. Therefore, this system has a solution, $(3,10)$, rather than no solution.

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

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

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

$y=10$

$y=10x+10$

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

$y=14x+14$

$y=10x+14$

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

$x=3$

$y=10$

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

$y=6x+3$

$y=6x+9$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-168"}