AlgebraStructure & Method · Book 1All Chapters

Using Two Variables

8-1Equations in Two Variables

Overview

An equation in two variables has solutions that are ordered pairs (x, y).

Key ideas

  • A solution makes the equation true when substituted.
  • There are usually infinitely many solutions.
  • Write solutions as (x, y).

Worked examples

Example 1

Problem. Is (2, 5) a solution of y = 2x + 1?

Solution. 2(2) + 1 = 5 ✓ Yes.

Example 2

Problem. Find a solution of y = 3x.

Solution. If x = 2, y = 6. So (2, 6).

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Is (1, 4) a solution of y = x + 3?

  2. 2.

    Find a solution of y = x − 2.

  3. 3.

    Is (−1, 0) a solution of y = 2x + 2?

Challenge problems

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

  1. 1.

    If y = 2x − 3, find y when x = −1, 0, and 2.

  2. 2.

    If 3x + 2y = 12, find y when x = 2 and when x = 4.