Systems of Linear Equations

Formulate, simplify, expand, and factor linear and polynomial expressions with rational coefficients using properties of operations.

Solve and verify one-step and two-step linear equations in forms such as px + q = r and p(x + q) = r with rational numbers fluently.

Solve multi-step linear equations with variables on both sides, clear fractions and decimals, solve literal equations, and determine solution cardinality.

Write, solve, and graph one-variable linear inequalities with rational numbers, and interpret solution sets within contextual constraints.

Understand the function concept as a single-output rule, distinguish variables, evaluate functions, and connect tables, equations, and graphs.

Analyze constant rates of change, determine and interpret slope and intercepts, and model real-world linear functions algebraically and graphically.

Solve systems of two linear equations in two variables graphically, by substitution, and by elimination, and model contextual problems.

Analyze non-linear relationships, explore quadratic functions and inverse proportional functions through tables, formulas, and graphs.

Solve introductory quadratic equations by square roots and factoring, and solve fractional algebraic equations while identifying extraneous roots.