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Algebra / Systems of two linear equations in two variables Difficulty: Easy

$x + y = 18$

$5 y equals x$

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

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Explanation

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.