{"status": "success", "data": {"description_md": "Let $S$ be the set of points $(x,y)$ in the coordinate plane such that two of the three quantities $3$, $x+2$, and $y-4$ are equal and the third of the three quantities is no greater than the common value. Which of the following is a correct description of $S$?\n\n$\\textbf{(A)}\\ \\text{a single point} \\qquad\\textbf{(B)}\\ \\text{two intersecting lines} \\qquad\\textbf{(C)}\\ \\text{three lines whose pairwise intersections are three distinct points} \\qquad\\textbf{(D)}\\ \\text{a triangle}\\qquad\\textbf{(E)}\\ \\text{three rays with a common point}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

Let S be the set of points (x,y) in the coordinate plane such that two of the three quantities 3, x+2, and y-4 are equal and the third of the three quantities is no greater than the common value. Which of the following is a correct description of S?

\\textbf{(A)}\\ \\text{a single point} \\qquad\\textbf{(B)}\\ \\text{two intersecting lines} \\qquad\\textbf{(C)}\\ \\text{three lines whose pairwise intersections are three distinct points} \\qquad\\textbf{(D)}\\ \\text{a triangle}\\qquad\\textbf{(E)}\\ \\text{three rays with a common point}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2017 AMC 12A Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p10", "prev": "/problem/17_amc12A_p08"}}