Substitution method

Math

Definition

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation. This reduces the system to a single equation with one variable.

How It Works

  1. Solve one equation for one variable in terms of the other.
  2. Substitute that expression into the other equation.
  3. Solve the resulting single-variable equation.
  4. Substitute back to find the value of the other variable.

Examples

  • Given y = 2x and x + y = 9: substitute to get x + 2x = 9, so x = 3, y = 6
  • Given 3x + y = 7 and x − y = 1: solve second for x: x = y + 1, then 3(y+1) + y = 7 → y = 1, x = 2

Related Terms

Elimination method Graphing systems Systems of three variables Solving systems with matrices

Study This Concept

Practice substitution method with free review games in these units:

Algebra 1 Unit 5: Systems of Equations