Chapter 9: Systems of Equations and Inequalities
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Course: MATH 142 (Precalculus II)
Overview
Systems of equations and matrix methods are powerful tools for solving problems with multiple unknowns. Partial fractions decomposition is essential for integration in calculus.
Source Material: OpenStax Precalculus Chapter 9 (CC BY 4.0)
Sections
| Section | Topic | Skills |
|---|---|---|
| 9.1 | Systems of Linear Equations: Two Variables | Substitution, elimination |
| 9.2 | Systems of Linear Equations: Three Variables | 3×3 systems |
| 9.3 | Systems of Nonlinear Equations and Inequalities | Curves intersecting |
| 9.4 | Partial Fractions | Decomposition techniques |
| 9.5 | Matrices and Matrix Operations | Addition, multiplication |
| 9.6 | Solving Systems with Gaussian Elimination | Row reduction |
| 9.7 | Solving Systems with Inverses | Matrix inverses |
| 9.8 | Solving Systems with Cramer’s Rule | Determinants |
Skills in This Chapter
What This Unlocks
Mastering systems and matrices prepares you for:
- Stewart 7.4: Partial fractions (integration technique)
- Stewart 15.6: Triple integrals (change of variables)
- Stewart 16.8: Stokes’ theorem (determinant form)
- MATH 241: Multiple integrals and Jacobians
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|---|---|---|
| Chapter 8 | Precalculus | Chapter 10 |