Variable (algebra)
A variable is a symbol, typically a letter such as x, y, or n, that represents an unknown or changing quantity in a mathematical expression or equation. Variables allow mathematicians to write general rules and relationships that apply to many specific cases at once. In algebra, manipulating variables to solve for unknowns or express patterns is the central skill.
Common Variable Conventions in Algebra
| Symbol | Typical Use | Example Expression | Notes |
|---|---|---|---|
| x | Unknown to solve for | 2x + 3 = 7 | Most common algebraic variable |
| y | Dependent variable | y = 3x − 1 | Often the output in a function |
| n | Integer or counting number | n² + n | Used in sequences and number theory |
| a, b, c | Constants or coefficients | ax² + bx + c | Parameters in general formulas |
| t | Time variable | d = vt | Common in physics-related algebra |
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Related Terms
Algebraic Expression
An algebraic expression is a combination of variables, constants, and arithmetic operations (addition, subtraction, multiplication, division, exponentiation) that represents a mathematical quantity without an equality sign. Unlike equations, expressions do not assert that two things are equal — they simply describe a value that depends on the variables present. Examples include 3x + 5, 2a² − 4b, and (x + y)/2.
Equation (algebra)
An algebraic equation is a mathematical statement asserting that two expressions are equal, connected by an equals sign (=). Solving an equation means finding the value(s) of the variable(s) that make the statement true, called the solution or root. Equations are fundamental to all branches of mathematics and science, providing a precise language for describing quantitative relationships.
Linear Equation
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the first power, producing a straight-line graph when plotted. The standard form of a linear equation in one variable is ax + b = 0, while in two variables it is ax + by = c. Linear equations are foundational in algebra and appear throughout science, economics, and engineering for modelling proportional relationships.
From Latin "variabilis" meaning "changeable", derived from "variare" (to vary). The use of letters for unknowns was popularised by French mathematician François Viète in the late 16th century, and the modern convention of using x for unknowns was established by René Descartes in 1637.