Chapter 5: Systems of Equations and Inequalities

The whole is more than the sum of its parts.
— Aristotle

Why This Matters

Real problems rarely involve a single equation. They involve systems — multiple equations that must all be true simultaneously.

  • Supply meets demand at equilibrium

  • Multiple forces balance at rest

  • Circuits obey Kirchhoff’s laws at every junction

Solving systems is finding where constraints intersect.

Sections

Section Topic Key Skill Status

5.1

Systems in Two Variables

Substitution, elimination

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5.2

Systems in Three Variables

Extended elimination

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5.3

Partial Fraction Decomposition

Break apart fractions

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5.4

Systems of Nonlinear Equations

Substitution strategies

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5.5

Systems of Inequalities

Graph solution regions

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5.6

Linear Programming

Optimize over constraints

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