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Check the Crossing

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 48 of 61.

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

Medium

The lines $y = x+5$ and $y = 2x+1$ cross at one point. Find its x and y.

Try it yourself

Find x, y

All lessons in Graphs & Systems

1Points and Rules

Two Numbers, One Point A Rule Makes Points The Points Line Up

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by DrawingCheck the CrossingWhen Lines Never Cross Recap: By Graphing

2The Whole Plane

The Four Quadrants Mirror Points On the Line or Not?Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods