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

$y=(x-2)(x+4)$

$y=6x-12$

Which ordered pair $(x,y)$ is the solution to the given system of equations?

","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-advanced-math-multiple-choice-question-110"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$y=(x-2)(x+4)$

$y=6x-12$

Which ordered pair $(x,y)$ is the solution to the given system of equations?

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

Choice C is correct. The second equation in the given system of equations is $y=6x-12$ Substituting $6x-12$ for $y$ in the first equation of the given system yields $6x-12=(x-2)(x+4)$ Factoring 6 out of the left-hand side of this equation yields $6(x-2)=(x-2)(x+4)$ An expression with a factor of the form $(x-a)$ is equal to zero when $x=a$. Each side of this equation has a factor of $(x-2)$, so each side of the equation is equal to zero when $x=2$. Substituting 2 for $x$ into the equation $6(x-2)=(x-2)(x+4)$ yields $6(2-2)=(2-2)(2+4)$, or $0=0$, which is true. Substituting 2 for $x$ into the second equation in the given system of equations yields $y=6(2)-12$, or $y=0$. Therefore, the solution to the system of equations is the ordered pair $(2,0)$.

Choice A is incorrect and may result from switching the order of the solutions for $x$ and $y$.

Choice B 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":"

$y=(x-2)(x+4)$

$y=6x-12$

Which ordered pair $(x,y)$ is the solution to the given system of equations?

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

$(0,2)$

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

$(-4,2)$

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

$(2,-4)$

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

$(2,0)$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-110"}

$y=(x-2)(x+4)$$y=6x-12$Which ordered pair $(x,y)$ is the solution to the given system of equations?

$y=(x-2)(x+4)$$y=6x-12$Which ordered pair $(x,y)$ is the solution to the given system of equations?

$y=(x-2)(x+4)$$y=6x-12$Which ordered pair $(x,y)$ is the solution to the given system of equations?

$y=(x-2)(x+4)$

$y=6x-12$

Which ordered pair $(x,y)$ is the solution to the given system of equations?

$y=(x-2)(x+4)$

$y=6x-12$

Which ordered pair $(x,y)$ is the solution to the given system of equations?

$y=(x-2)(x+4)$

$y=6x-12$

Which ordered pair $(x,y)$ is the solution to the given system of equations?