AlgebraStructure & Method · Book 1All Chapters

Solving Systems of Linear Equations

9-3Solving Problems with Two Variables

Overview

Use two variables and two equations to model two-quantity problems.

Key ideas

  • Assign a variable to each unknown.
  • Write two equations from the conditions.
  • Solve and check.

Worked examples

Example 1

Problem. Sum 30, difference 6. Find the numbers.

Solution. x + y = 30, x − y = 6 → x = 18, y = 12.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Sum 50, difference 10. Find numbers.

  2. 2.

    Sum 24, twice one is the other. Find them.

  3. 3.

    Sum 100, difference 40.

Challenge problems

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

  1. 1.

    The sum of two numbers is 25 and their difference is 7. Find the numbers.

  2. 2.

    A theater sold 250 tickets for $1550. Adult tickets are $8, child tickets are $5. How many of each?