Solving Systems of Linear Equations

9-4The Addition-or-Subtraction Method

Overview

Add or subtract equations to eliminate one variable.

Key ideas

  • Line up like terms.
  • Add to cancel opposites; subtract to cancel matches.
  • Solve, then back-substitute.

Worked examples

Example 1

Problem. x + y = 7 and x − y = 1.

Solution. Add: 2x = 8 → x = 4, y = 3.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    x + y = 10, x − y = 4.

  2. 2.

    2x + y = 11, x − y = 1.

  3. 3.

    3x + y = 12, 3x − y = 0.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Solve: 2x + 3y = 13 and 2x − y = 5.

  2. 2.

    Solve: 3x + 2y = 12 and 5x − 2y = 4.