Elimination method

Math

Definition

The elimination method solves a system of linear equations by adding or subtracting the equations to eliminate one variable. You may need to multiply one or both equations by a constant first so that one variable's coefficients are opposites.

How It Works

  1. Align the equations with like terms in columns
  2. Multiply one or both equations so one variable has opposite coefficients
  3. Add the equations to eliminate that variable
  4. Solve for the remaining variable
  5. Substitute back to find the other variable

Examples

  • Solving 2x + y = 7 and x - y = 2 by adding: 3x = 9, so x = 3
  • Multiplying x + 2y = 5 by 3 and 3x - y = 4 by 1, then subtracting
  • Finding the price of two items given total costs of different combinations

Related Terms

Substitution method Graphing systems Systems of three variables

Study This Concept

Practice elimination method with free review games in these units:

Algebra 1 Unit 5: Systems of Equations