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

The graph of a system of an absolute value function and a linear function is shown. What is the solution $(x, y)$ to this system of two equations?

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Explanation

Choice C is correct. The solution to a system of two equations corresponds to the point where the graphs of the equations intersect. The graphs of the linear function and the absolute value function shown intersect at a point with an x-coordinate between $negative 4$ and $negative 3$ and a y-coordinate between $4$ and $5$ . Of the given choices, only $(- \frac{7}{2}, \frac{9}{2})$ has an x-coordinate between $negative 4$ and $negative 3$ and a y-coordinate between $4$ and $5$ .

Choice A is incorrect. This is the y-intercept of the graph of the linear function.

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

Choice D is incorrect. This is the vertex of the graph of the absolute value function.