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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Easy

$y equals 76$
$y = x^{2} - 5$

The graphs of the given equations in the xy-plane intersect at the point $(x, y)$ . What is a possible value of $x$ ?

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Explanation

Choice B is correct. Since the point $(x, y)$ is an intersection point of the graphs of the given equations in the xy-plane, the pair $(x, y)$ should satisfy both equations, and thus is a solution of the given system. According to the first equation, $y equals 76$ . Substituting $76$ in place of $y$ in the second equation yields $x^{2} - 5 = 76$ . Adding $5$ to both sides of this equation yields $x squared equals 81$ . Taking the square root of both sides of this equation yields two solutions: $x equals 9$ and $x = - 9$ . Of these two solutions, only $negative 9$ is given as a choice.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the value of coordinate $y$ , rather than $x$ , of the intersection point $(x, y)$ .