Two Lines, One Answer

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 47 of 64.

Two equations asked together are a system, and on the plane a system is two lines. A point that satisfies both equations must lie on both lines, and two crossing lines share exactly one point: the crossing IS the solution.

$The crossing (1, 2) solves both equations at once$

The crossing (1, 2) solves both equations at once

Check it: at (1, 2), y = x + 1 reads 2 = 2 and y = -x + 3 reads 2 = 2. One point, two true equations; that is what "solving a system" means.

Challenge

Two lines are drawn. Place the point that solves both of their equations at once.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This 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 Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

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 AnswerSolve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes Points The Points Line Up On the Line or Not?Between the Dots 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