When Lines Never Cross
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 52 of 64.
Two lines do not always cross. Parallel lines have the same slope and different intercepts, so they share no point. A system of two parallel lines has no solution. For example, x + y = 3 and x + y = 7 cannot both be true. No pair of numbers adds to 3 and to 7 at the same time. The algebra shows it too. Subtracting the first equation from the second leaves 0 = 4, which is false.
Equivalent equations describe the same line. For example, 4x + 2y = 10 is twice 2x + y = 5, so every point on that line satisfies both. The system has infinitely many solutions. Two distinct intersecting lines have one solution, and two distinct parallel lines have none.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs & Systems
1The Coordinate Plane
Two Numbers, One PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations10Systems by Graphing
Two Lines, One AnswerSolve by DrawingCheck the CrossingWhen Lines Never CrossRecap: By Graphing2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line