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

$x equals 5$

$y = x - 8$

Which of the following points $(x, y)$ is the solution to the given system of equations in the xy-plane?

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Explanation

Choice B is correct. A solution to a system of equations in the xy-plane is a point $(x, y)$ that lies on the graph of each equation in the system. The first equation given is $x equals 5$ . Substituting $5$ for $x$ in the second given equation yields $y = 5 - 8$ , or $y = - 3$ . It follows that in the xy-plane, the point $left parenthesis 5 comma negative 3 right parenthesis$ lies on the graph of each equation in the system. Therefore, the solution to the given system of equations in the xy-plane is $left parenthesis 5 comma negative 3 right parenthesis$ .

Choice A is incorrect. The point $left parenthesis 0 comma 0 right parenthesis$ doesn't lie on the graph of either equation in the given system.

Choice C is incorrect. The point $left parenthesis 5 comma negative 8 right parenthesis$ doesn't lie on the graph of the second equation in the given system.

Choice D is incorrect. The point $left parenthesis 5 comma 8 right parenthesis$ doesn't lie on the graph of the second equation in the given system.