Public learning track
Simultaneous Equations and Nonlinear Systems
11th Grade · Math · Open Global Math
6 lessons
Goal
Solve simultaneous linear and nonlinear systems in two variables algebraically and interpret solutions geometrically.
Featured Diagrams
Solving Linear Systems by Algebraic Substitution and Elimination
6 lessons
0 of 6 done
- 1Solving Linear Systems by Algebraic Substitution and EliminationUp nextStart
- 2Solving Linear and Quadratic Simultaneous Equations AlgebraicallyPremiumNot started yet
- 3Solving Systems of Lines and CirclesNot started yet
- 4Solving Simultaneous Quadratic SystemsNot started yet
- 5Geometric Interpretation and Tangency Conditions in SystemsNot started yet
- 6Modeling Real-World Scenarios with Nonlinear SystemsNot started yet
Standards Covered
- OGM.12.ALG.4Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Solve simultaneous equations in two variables (including linear-quadratic systems) by substitution and elimination, and solve/graph linear and quadratic inequalities using set and interval notation.
- OGM.12.ALG.3Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Solve quadratic equations in a function of the unknown, utilize the discriminant to determine root nature, and complete the square to analyze quadratic forms and optimize objective functions.
Curriculum Framework
11th Grade · Math · Open Global Math
1
9 lessons
Polynomial Theorems, Division, and Advanced Factoring
Master polynomial operations, algebraic long division, the Remainder and Factor Theorems, and factoring techniques for higher-degree polynomials.
2
5 lessons
Rational Expressions and Algebraic Fractions
Simplify, add, subtract, multiply, and divide complex rational expressions and simplify compound algebraic fractions.
3
6 lessons
Partial Fraction Decomposition
Decompose proper and improper rational expressions into partial fractions with distinct linear, repeated linear, and irreducible quadratic denominators.
4
6 lessons
Advanced Quadratic Forms, Discriminant, and Optimization
Analyze quadratic forms using discriminant analysis, solve equations reducible to quadratics, and optimize objective functions via completing the square.
5
6 lessons
Simultaneous Equations and Nonlinear Systems
Solve simultaneous linear and nonlinear systems in two variables algebraically and interpret solutions geometrically.
6
6 lessons
Linear and Quadratic Inequalities
Solve single-variable linear and quadratic inequalities, graph two-variable inequality regions, and express solution sets using interval and set notation.
7
5 lessons
Binomial Theorem with Positive Integers
Expand binomial expressions with positive integer powers using Pascal's triangle, combinatorics, and sigma notation.
8
6 lessons
General Binomial Series and Rational Exponents
Expand (1 + x)ⁿ and (a + bx)ⁿ for any rational exponent n, determine radius of convergence, and perform numerical approximations.