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Title: How Many Points Do Two Lines Intersect At? (Simplified Explanation) 　　Answer: Two straight lines in a plane intersect at one point unless they are parallel or coinciding. 　　Explanation: General Case: In Euclidean geometry, two distinct lines intersect at exactly one point (Figure 1). Example: Line ( y = 2x + 1 ) and ( y = -x + 3 ) intersect at ( (1, 3) ). Special Cases: Parallel Lines: No intersection (Figure 2). Example: ( y = 2x + 1 ) and ( y = 2x - 4 ). Coinciding Lines: Infinitely many intersections (Figure 3). Example: ( y = 2x + 1 ) and ( 2y = 4x + 2 ). 　　Visualizations (for reference): Figure 1: Two intersecting lines. Figure 2: Two parallel lines. Figure 3: Two overlapping lines. 　　Key Formula (for coordinates): If two lines are ( a_1x + b_1y + c_1 = 0 ) and ( a_2x + b_2y + c_2 = 0 ), their intersection is: [ \left( \frac{b_1c_2 - b_2c_1}{a_1b_2 - a_2b_1}, \frac{a_2c_1 - a_1c_2}{a_1b_2 - a_2b_1} \right) ] (Valid only if the denominator ( \neq 0 )). 　　Common Pitfall: Assuming all lines intersect in a game. Always check for parallel/coinciding conditions first! 　　Application in Games: Use this logic for puzzles involving line intersections (e.g., grid-based games, geometry challenges). 　　Let me know if you need further clarification! 😊