# Variable Definition

In Mathematics, an algebraic expression is an expression which consists of the combination of variables, constants, coefficients, fundamental operations such as addition, subtraction, multiplication and division. Each term constitutes the basis of algebra. In this article, let us discuss the term “**Variable**” in detail. Here, the variable definition, types of variables, its properties and examples are explained.

## Variable Definition in Maths

In Algebra, a variable is an alphabet which is used to represent the unknown number. It represents the value. A variable is a quantity that may be changed according to the mathematical problem. The generic letters which are used in many algebraic expressions and equations are x, y, z. In other words, a variable is a symbol for a number where the value is not known.

For example, x + 5 = 10

Here “x” is a variable.

The value of the variable “x” can be easily found by solving the equation. In this case, if the equation is solved, the value of the variable “x” is obtained as 5. It means that x = 5.

Similarly, the term variable is used in Statistics also. In Statistics, a variable may be sometimes called a data item. It represents the number/characteristics that can be measured. For example, sex, age, income, capital expenditure are examples of variables in Statistics

## Types of Variables

Variables are broadly classified into two categories, namely:

**Dependent Variable**

The dependent variable is a variable that depends on the value of some other number or variable. In short, the dependent variable is the output of a function. The value of the dependent variable changes, if there is a change in the value of an independent variable. The variable is dependent because its value depends on what we put into the function.

Example: y = 4 + 2x

Here, y is called a dependent variable. The value of y completely depends on the function 4 + 2x

**Independent Variable**

The independent variable does not depend on any values. It is called the input of a function. The value of the independent variable is not affected by any values of a function.

Example: x = 2y + 3z

Here, x is called a dependent variable

y and z are the independent variables

Because the value of y and z are not affected by any other values.

### Variable Example

**Question: **

Find the value of the variable y for the equation y = 2x^{2} when x = 5

**Solution:**

Given equation: y = 2x^{2}

Here x is called independent variable

Y is called dependent variable

When x = 5, the value of y becomes:

y = 2x^{2}

Now, substituting x = 5 in the given equation, we get

y = 2(5)^{2 }

y = 2(25)

y = 50

Therefore, the value of y is 50, when x = 5

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