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Systems of Equations

Overview

Where two lines cross.

What is it?

Finding the single point (x, y) that works for two different equations.

History

Used in economics to find where Supply meets Demand.

Key Idea

Substitution or Elimination: pick your weapon.

Practice This Topic

Concept Guide

Plain English: A system asks: 'When will these two things be equal?' It's solving two puzzles at once to find the one answer that fits both.

Real-world example: Comparing two cell phone plans to see which is cheaper for your usage.

Common Pitfall

Finding X but forgetting to plug it back in to find Y.

Word Problem
"Plan A: $10/mo. Plan B: $5/mo + $20 setup. When do they cost the same?"
Reasoning: 10x = 5x + 20. 5x = 20. x = 4 months.

Practice Examples

Intersection
y = x y = 2 - x Point: (1, 1)
Where lines cross.