Linear equation

A linear equation is an equality in which each variable appears only to the first power and variables are not multiplied together. Its solutions form a line, plane, or higher-dimensional flat.

Linear expression: An algebraic expression formed from constants and variables with variables appearing only to the first power. Its terms become the two sides or components of a linear equation.
Equivalent equations: Equations with the same solution set. Each valid rearrangement of a linear equation should preserve its solutions.
System of linear equations: A collection of linear equations that must hold for the same unknown values. Several simultaneous constraints form a system rather than one equation.
Quadratic equation: An equation whose polynomial terms have degree at most two, with at least one quadratic term. A squared variable makes a quadratic equation nonlinear.
One-variable linear equation: An equation of the form ax + b = 0, where a and b are constants and a is nonzero. It is the simplest case, with exactly one solution.
Equation: A mathematical statement asserting that two expressions are equal. A linear equation is the special case with first-degree variable terms.
Inverse operation: An operation that reverses the effect of another operation. Inverse operations isolate a variable without changing the equation’s solutions.
Linear programming: Optimization of a linear objective subject to linear equality and inequality constraints. Its equality constraints are linear equations defining feasible solutions.
Nonlinear equation: An equation whose variables do not satisfy the defining conditions of a linear equation. It is the broader contrasting class, including polynomial and transcendental equations.
Two-variable linear equation: An equation of the form ax + by = c, with constants a, b, and c. Its solutions generally form a straight line in the coordinate plane.

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