AlgebraStructure & Method · Book 1All Chapters

Solving Systems of Linear Equations

9-5Multiplication with the Addition-or-Subtraction Method

Overview

Multiply one or both equations to create opposite coefficients, then add.

Key ideas

  • Pick a variable to eliminate.
  • Multiply each equation so its coefficient becomes opposite the other’s.
  • Add to eliminate; solve.

Worked examples

Example 1

Problem. 2x + 3y = 12; x − y = 1.

Solution. Multiply 2nd by 3: 3x − 3y = 3. Add: 5x = 15 → x = 3, y = 2.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    x + 2y = 7; 3x − y = 7.

  2. 2.

    2x + y = 5; 3x − 2y = 4.

  3. 3.

    4x + 3y = 18; 2x − y = 2.

Challenge problems

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

  1. 1.

    Solve: 2x + 3y = 7 and 3x − 2y = 4.

  2. 2.

    Solve: 4x + 3y = 11 and 2x − y = 7.