Graphing systems

Math

Definition

A method of solving a system of equations by graphing each equation on the same coordinate plane and finding the point(s) where the graphs intersect. The intersection point represents the solution that satisfies all equations simultaneously.

How It Works

  1. Rewrite each equation in a form suitable for graphing (such as slope-intercept form).
  2. Graph the first equation on the coordinate plane.
  3. Graph the second equation on the same coordinate plane.
  4. Identify the point(s) of intersection.
  5. Verify the solution by substituting into both original equations.

Examples

  • Graphing y = 2x + 1 and y = −x + 4 shows they intersect at (1, 3)
  • Parallel lines like y = 2x + 1 and y = 2x − 3 have no solution
  • Identical lines have infinitely many solutions

Related Terms

Substitution method Elimination method Slope-intercept form

Study This Concept

Practice graphing systems with free review games in these units:

Algebra 1 Unit 5: Systems of Equations