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Solve by Drawing

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 48 of 64.

Solving by graphing is just drawing both lines and reading the crossing. For y = 2x - 3; y = -x + 3: the first crosses at (0, -3) climbing 2, the second crosses at (0, 3) falling 1, and they meet at (2, 1). That meeting point is the answer, x = 2 and y = 1.

The method is honest but rough: a crossing at (2, 1) reads cleanly, a crossing at thirds does not. Graphing shows WHERE the answer is; the next chapter computes it exactly, whatever it is.

Challenge

Draw both lines of the system y = x - 1; y = -2x + 5 and see where they meet.

Try it yourself

y = x - 1y = -2x + 5

Draw the graph

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 DrawingCheck 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