Check the Crossing
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 51 of 64.
After you read a crossing off a graph, check it by substituting it into both equations. For the system y = x + 2 and y = 3x - 2, substitute the point (2, 4). The first equation gives 4 = 2 + 2 and the second gives 4 = 6 - 2. Both are true, so (2, 4) is the solution. A point that satisfies one equation but not the other lies on one line only. It is not a solution of the system.
You can also find the crossing without a drawing. Where the two lines meet, they have the same y, so their right sides are equal. That gives x + 2 = 3x - 2, an equation in x alone. Its solution is the x-coordinate of the crossing.
Challenge
MediumThe lines y = x + 5 and y = 2x + 1 cross at one point. Find its x and y.
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