#AP SAT (Digital) Math: Systems of Linear Equations - Your Night-Before Guide

Hey there, future math master! Let's get you prepped and confident for the AP SAT (Digital) Math section on systems of linear equations. This guide is designed to be your quick, go-to resource for a final review. Let's make sure everything clicks!

#1. Setting Up Linear Equations from Word Problems

#1.1 Identifying and Representing Unknown Quantities

• What are they? Systems of linear equations are just two or more equations with the same variables. Think of them as a puzzle where you need to find the values of those variables.
• Word Problem Clue: If a word problem has two unknown things that are related, that's your cue to use a system of equations!
• The Game Plan:
  • Assign variables (usually x and y) to represent the unknowns. 💡
  • Read the problem super carefully, noting how these unknowns relate to each other or to known numbers.
  • Translate those words into math equations.
• Example: "The sum of two numbers is 10" becomes x + y = 10

#1.2 Creating Accurate Equations

• Key Rule: The number of equations needs to match the number of unknowns. Two unknowns? You need two equations!
• Double-Check: Make sure your equations actually match the relationships described in the problem.
• Consistency is Key: Ensure your equations make sense with the problem statement.
• Don't Miss Anything: Include all the relevant info from the problem in your equations.