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Solve by Drawing

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 47 of 61.

To solve a system by graphing, draw both lines and read where they cross. Take $y = 2x-3;\quad y = -x+3$ . The first line crosses the y-axis at (0, -3) and has slope 2. The second line crosses the y-axis at (0, 3) and has slope -1. The two lines meet at (2, 1). That point is the solution, $x = 2$ and $y = 1$ .

An intersection at $\left(2, 1\right)$ can be read from the grid. If the intersection falls between grid marks, its coordinates may be difficult to read accurately. Algebraic methods can give the exact solution.

Challenge

Medium

Draw both lines of $y = x-3;\quad y = -3x+5$ and read off where they cross.

Try it yourself

y = x-3

y = -3x+5

Draw both lines

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 AnswerSolve by DrawingCheck the Crossing When 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