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

$y=x^{2}$

$2y+6=2(x+3)$

If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

","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-161"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$y=x^{2}$

$2y+6=2(x+3)$

If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

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

Choice A is correct. Substituting $x^{2}$ for $y$ in the second equation gives $2(x^{2})+6=2(x+3)$. This equation can be solved as follows:

$2x^{2}+6=2x+6$ (Apply the distributive property.)

$2x^{2}+6-2x-6=0$ (Subtract $2x$ and $6$ from both sides of the equation.)

$2x^{2}-2x=0$ (Combine like terms.)

$2x(x-1)=0$ (Factor both terns on the left side of the equation by $2x$

Thus, $x=0$ and $x=1$ are the solutions to the system. Since $x>0$, only $x=1$ needs to be considered. The value of y when $x=1$ is $y=x^{2}=1^{2}=1$. Therefore, the value of $xy$ is $(1)(1)=1$.

Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.

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

$y=x^{2}$

$2y+6=2(x+3)$

If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

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

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

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

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

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

Choice A is correct. Substituting $x^{2}$ for $y$ in the second equation gives $2(x^{2})+6=2(x+3)$. This equation can be solved as follows:

$2x^{2}+6=2x+6$ (Apply the distributive property.)

$2x^{2}+6-2x-6=0$ (Subtract $2x$ and $6$ from both sides of the equation.)

$2x^{2}-2x=0$ (Combine like terms.)

$2x(x-1)=0$ (Factor both terns on the left side of the equation by $2x$

Thus, $x=0$ and $x=1$ are the solutions to the system. Since $x>0$, only $x=1$ needs to be considered. The value of y when $x=1$ is $y=x^{2}=1^{2}=1$. Therefore, the value of $xy$ is $(1)(1)=1$.

Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.

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

Choice A is correct. Substituting $x^{2}$ for $y$ in the second equation gives $2(x^{2})+6=2(x+3)$. This equation can be solved as follows:

$2x^{2}+6=2x+6$ (Apply the distributive property.)

$2x^{2}+6-2x-6=0$ (Subtract $2x$ and $6$ from both sides of the equation.)

$2x^{2}-2x=0$ (Combine like terms.)

$2x(x-1)=0$ (Factor both terns on the left side of the equation by $2x$

Thus, $x=0$ and $x=1$ are the solutions to the system. Since $x>0$, only $x=1$ needs to be considered. The value of y when $x=1$ is $y=x^{2}=1^{2}=1$. Therefore, the value of $xy$ is $(1)(1)=1$.

Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-161"}

$y=x^{2}$$2y+6=2(x+3)$If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

$y=x^{2}$$2y+6=2(x+3)$If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

$y=x^{2}$$2y+6=2(x+3)$If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

$y=x^{2}$

$2y+6=2(x+3)$

If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

$y=x^{2}$

$2y+6=2(x+3)$

If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

$y=x^{2}$

$2y+6=2(x+3)$

If $\\{x,y\\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

$y=x^{2}$$2y+6=2(x+3)$If $\{x,y\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?

$y=x^{2}$

$2y+6=2(x+3)$

If $\{x,y\}$ is a solution of the system of equations above and $x>0$, what is the value of $xy$ ?