When Lines Never Cross
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 50 of 64.
Two lines need not cross. Parallel lines, same slope and different intercepts, share no point at all, so their system has no solution: x + y = 3 and x + y = 7 cannot both hold, no pair sums to 3 and to 7 at once. The algebra says it too: subtracting the equations leaves 0 = 4, false.
And two equations can be the SAME line in two costumes, like 2x + y = 5 and 4x + 2y = 10: every point of the line solves both, infinitely many solutions. Crossing lines, parallel lines, one line twice: one solution, none, or all of them.
Challenge
Try to solve the system x + y = 3; x + y = 7 and see what the algebra says.
Try it yourself
Solve for x,y
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