Question: A museum curator arranges two exhibit pathways modeled by the lines $ y = 4x - 5 $ and $ 2y + 3x = 10 $. Find their intersection point.

["Title: Finding the Intersection of Two Exhibit Pathways in the Museum: A Step-by-Step Analysis of the Lines $ y = 4x - 5 $ and $ 2y + 3x = 10 $", "---", "Introduction\nImagine wandering through a modern art museum where two elegant exhibit pathways define contrasting tones and movements—represented mathematically by intersecting lines. In this scenario, a curator strategically arranges two pathways modeled by the equations $ y = 4x - 5 $ and $ 2y + 3x = 10 $. Understanding where these paths meet enriches the visitor experience and reveals the harmony of geometry embedded in cultural spaces. In this article, we explore how to find the exact point of intersection between these two lines—a fundamental technique useful in art layout design, navigation systems, and architectural planning.", "---", "Understanding the Problem\nThe curator’s challenge is to determine the coordinates where the two exhibit lines cross. Mathematically, this means solving the system of equations:\n1. $ y = 4x - 5 $\n2. $ 2y + 3x = 10 $", "These lines represent distinct gallery routes; their intersection marks a pivotal meeting point designed for social interaction, seating, or scenic unveiling of artworks.", "---", "Step 1: Substitute the Expression for $ y $\nSince the first equation provides $ y $ explicitly, substitution simplifies solving the system. Replace $ y $ in the second equation with $ 4x - 5 $:\n[\n2(4x - 5) + 3x = 10\n]", "---", "Step 2: Expand and Simplify the Equation\nDistribute the 2 across the parentheses:\n[\n8x - 10 + 3x = 10\n]\nCombine like terms:\n[\n11x - 10 = 10\n]\nAdd 10 to both sides:\n[\n11x = 20\n]\nSolve for $ x $:\n[\nx = \frac{20}{11}\n]", "---", "Step 3: Substitute Back to Find $ y $\nNow, substitute $ x = \frac{20}{11} $ into $ y = 4x - 5 $:\n[\ny = 4\left(\frac{20}{11}\right) - 5 = \frac{80}{11} - \frac{55}{11} = \frac{25}{11}\n]", "---", "Conclusion\nThe two exhibit pathways intersect at the precise point\n[\n\left( \frac{20}{11},\ \frac{25}{11} \right)\n]\nThis intersection coordinates serve not just as a mathematical milestone but as a curated space within the museum—where art, architecture, and geometry coalesce. By finding where $ y = 4x - 5 $ meets $ 2y + 3x = 10 $, the curator thoughtfully shapes the visitor journey, turning abstract coordinates into a vibrant cultural destination.", "For designers, artists, and museum developers, understanding linear intersections offers a powerful tool for crafting intentional, engaging spatial experiences. Thus, the mathematical intersection of two lines becomes more than a curve on a graph—it becomes a moment of human connection within the museum’s narrative.", "---", "Keywords: museum exhibit pathways, intersection of lines, linear equations, curator design, coordinate geometry, museum navigation, algebra in architecture, intersecting paths, geometry in art spaces", "Meta Description:\nDiscover how a museum curator finds the intersection of two exhibit pathways modeled by $ y = 4x - 5 $ and $ 2y + 3x = 10 $. Learn step-by-step methods for solving linear equations and explore the practical application in art and design.", "---", "Checklist for Museum Planners:\n- Use linear equations to define pathway routes\n- Solve intersections using substitution for precision\n- Mark intersection points as key social hubs\n- Enhance visitor flow through geometric planning", "---", "Next time you walk through a museum, imagine the invisible math guiding your journey—where every turn, every curve, is a carefully plotted moment of inspiration."]