Question #317e80f9 - SAT Suite Question Bank

ID: 317e80f9

Modded SAT Question Bank by Abdullah Mallik

$x + y = 18$

$5 y equals x$

What is the solution $(x, y)$ to the given system of equations?

$left parenthesis 15 comma 3 right parenthesis$
$left parenthesis 16 comma 2 right parenthesis$
$left parenthesis 17 comma 1 right parenthesis$
$left parenthesis 18 comma 0 right parenthesis$

Toggle Answer

Tip: Press CTRL/Command to toggle answer

Correct Answer: A

Rationale

Choice A is correct. The second equation in the given system defines the value of $x$ as $5 y$ . Substituting $5 y$ for $x$ into the first equation yields $5 y + y = 18$ or $6 y equals 18$ . Dividing each side of this equation by $6$ yields $y equals 3$ . Substituting $3$ for $y$ in the second equation yields $5 left parenthesis 3 right parenthesis equals x$ or $x equals 15$ . Therefore, the solution $(x, y)$ to the given system of equations is $left parenthesis 15 comma 3 right parenthesis$ .

Choice B is incorrect. Substituting $16$ for $x$ and $2$ for $y$ in the second equation yields $5 left parenthesis 2 right parenthesis equals 16$ , which is not true. Therefore, $left parenthesis 16 comma 2 right parenthesis$ is not a solution to the given system of equations.

Choice C is incorrect. Substituting $17$ for $x$ and $1$ for $y$ in the second equation yields $5 left parenthesis 1 right parenthesis equals 17$ , which is not true. Therefore, $left parenthesis 17 comma 1 right parenthesis$ is not a solution to the given system of equations.

Choice D is incorrect. Substituting $18$ for $x$ and $0$ for $y$ in the second equation yields $5 left parenthesis 0 right parenthesis equals 18$ , which is not true. Therefore, $left parenthesis 18 comma 0 right parenthesis$ is not a solution to the given system of equations.

Question Difficulty: Easy