Public learning track
Systems of Linear Equations in Two and Three Variables
9th Grade · Math · Open Global Math
9 lessons
Goal
Solve systems of linear equations in two and three variables using graphing, substitution, and elimination, and prove equivalence under linear combinations.
Featured Diagrams
Solving Systems of Linear Equations by Graphing
9 lessons
0 of 9 done
- 1Solving Systems of Linear Equations by GraphingUp nextStart
- 2Interpreting Simultaneous Equation Solutions GraphicallyPremiumNot started yet
- 3Solving Linear Systems by Algebraic SubstitutionNot started yet
- 4Solving Linear Systems by Algebraic Elimination (Addition and Subtraction)Not started yet
- 5Proving Equivalence of Linear Systems Under Linear CombinationsNot started yet
- 6Representing Three-Variable Linear Equations as PlanesNot started yet
- 7Solving Systems of Three Linear Equations Using Successive EliminationNot started yet
- 8Classifying Inconsistent and Dependent Three-Variable Linear SystemsNot started yet
- 9Modeling Real-World Scenarios with Systems in Two and Three VariablesNot started yet
Curriculum Framework
9th Grade · Math · Open Global Math
1
11 lessons
Linear Equations, Literal Formulas, and Single-Variable Inequalities
Solve multi-step linear equations and inequalities with numerical and literal coefficients, justify each algebraic transformation, and rearrange scientific formulas for specified variables.
2
7 lessons
Quadratic Equations: Factoring, Square Roots, and Completing the Square
Solve quadratic equations using the zero-product property, square root extraction, and completing the square for monic and non-monic quadratics.
3
8 lessons
The Quadratic Formula, Discriminant Analysis, and Vieta's Relations
Solve any quadratic equation using the quadratic formula, analyze root types and multiplicities using the discriminant, and relate roots to coefficients using Vieta's formulas.
4
10 lessons
Radical, Rational, and Absolute Value Equations and Inequalities
Solve simple rational, radical, and absolute value equations and inequalities in one variable, and identify extraneous solutions introduced by algebraic operations.
5
9 lessons
Systems of Linear Equations in Two and Three Variables
Solve systems of linear equations in two and three variables using graphing, substitution, and elimination, and prove equivalence under linear combinations.
6
7 lessons
Matrix Methods and Gaussian Elimination for Linear Systems
Solve systems of linear equations using augmented matrices, row echelon transformations (Gaussian elimination), and matrix inverses (AX = B).
7
7 lessons
Non-Linear and Linear-Quadratic Systems of Equations
Solve systems involving linear, quadratic, and circular equations in two variables algebraically and graphically, and interpret points of intersection.
8
8 lessons
Two-Variable Linear Inequalities and Feasible Regions in Optimization
Graph linear inequalities in two variables as half-planes, identify polygonal feasible regions for systems of linear inequalities, and interpret constraints and viable solutions in modeling contexts.