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

If a new graph of three linear equations is created using the system of equations shown and the equation $x+4y=-16$, how many solutions $(x,y)$ will the resulting system of three equations have?

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","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-265"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

If a new graph of three linear equations is created using the system of equations shown and the equation $x+4y=-16$, how many solutions $(x,y)$ will the resulting system of three equations have?

$\"\"$

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

Choice A is correct. A solution to a system of equations must satisfy each equation in the system. It follows that if an ordered pair $x,y$ is a solution to the system, the point $x,y$ lies on the graph in the $xy$-plane of each equation in the system. The only point that lies on each graph of the system of two linear equations shown is their intersection point $8,2$). It follows that if a new graph of three linear equations is created using the system of equations shown and the graph of $x+4y=-16$, this system has either zero solutions or one solution, the point $8,2$). Substituting $8$ for $x$ and $2$ for $y$ in the equation $x+4y=-16$ yields $8+4(2)=-16$, or $16=-16$. Since this equation is not true, the point $(8,2)$ does not lie on the graph of $x+4y=-16$. Therefore, $(8,2)$ is not a solution to the system of three equations. It follows that there are zero solutions to this system.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

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

If a new graph of three linear equations is created using the system of equations shown and the equation $x+4y=-16$, how many solutions $(x,y)$ will the resulting system of three equations have?

$\"\"$

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

Exactly one

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

Exactly two

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

Infinitely many

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

Zero

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

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

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

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-265"}