Unit 9

Systems, Matrices, and Inequalities

Solve systems of linear and nonlinear equations and inequalities. Apply matrices and Gaussian elimination.

Unit 9 · 10 pages

Lessons

Unit overview, essential questions, learning objectives, and vocabulary list for Unit 9 Systems of Equations & Inequalities.

Solve 2×2 linear systems by substitution, elimination, and graphing; classify consistent and inconsistent systems.

Solve 3×3 linear systems using elimination; identify dependent and inconsistent systems.

Solve nonlinear systems by substitution and elimination; graph systems of inequalities.

Decompose rational expressions into partial fractions for distinct linear, repeated, and quadratic factors.

Add, subtract, and multiply matrices; apply scalar multiplication and understand dimension compatibility.

Use augmented matrices and row operations to reduce to row-echelon and reduced row-echelon form.

Find matrix inverses and use AX = B → X = A⁻¹B to solve linear systems.

Compute 2×2 and 3×3 determinants and apply Cramer's Rule to solve linear systems.

Consolidate your understanding of systems of equations, matrices, Gaussian elimination, and Cramer's Rule.