Variable definition

An algebraic expression is a mathematical expression made up of variables, constants, coefficients, and fundamental operations including addition, subtraction, multiplication, and division. Each phrase is the foundation of algebra. In this article we will discuss variables in detail.

Meaning of variable 

A variable is an alphabet in Algebra that is used to represent an unknown integer. It represents the worth of something. A variable is a quantity that can be altered to solve a mathematical issue. The letters x, y, and z are generic letters that are employed in many mathematical expressions and equations. A variable, in other terms, is a symbol denoting a number whose value is unknown.

For instance, x + 5 = 10.

“x” is a variable in this case.

By solving the equation, the value of the variable “x” can be easily determined. If the equation is solved in this situation, the value of the variable “x” is 5. This means that x equals 5.

Similarly, in Statistics, the term variable is employed. A variable is also known as a data item in statistics. It denotes the amount of variables or qualities that can be measured. Variables in Statistics include things like gender, age, income, and capital expenditure.

Types of variable 

There are various types of variables in mathematics but all of these variables are broadly divided into two categories :-

1. Dependent variable
2. Independent variable

Dependent variable

A dependent variable is one whose value is determined on the value of another number or variable. In a nutshell, the dependent variable is the function’s output. If the value of an independent variable changes, the value of the dependent variable changes as well. The variable is dependent because the value of the variable is determined by the input to the function.

For instance, y = 4 + 2x

Y is referred to as a dependent variable in this case. The function 4 + 2x entirely determines the value of y.

Independent variable

The independent variable isn’t affected by any of the values. A function’s input is what it’s called. The value of the independent variable is unaffected by the function’s values.

Suppose we have X = 2y + 3z, 

X is referred to as a dependent variable in this case.

The independent variables are y and z.

Because any other variables have no effect on the values of y and z.

A function is a rule for taking a number or set of numbers as input and creating an output, which could also be a number or collection of numbers, in mathematics. The most common character for input is x, and the most common character for output is y. As a result, the function is expressed as y = f. (x). An independent variable is a letter that represents a random input, such as x, whereas a dependent variable is a symbol that represents an arbitrary output, such as y in this case.

For example

When x = 8 , find the value of the variable y in the equation y = 2x².

Solution:

Y = 2x² is the given equation.

Here, x is referred to as an independent variable.

The dependent variable is Y.

When x equals 8, the value of y is:

Y = 2x² 

Substituting x = 8 into the given equation now yields

Y = 2 × (8)²

Y =. 2 × 64

Y = 128

As a result, when x = 8 , the value of y gives 128.

Conclusion :-

Variable is the letter or phrase in mathematics that is used to denote the unknown number, unknown value, or unknown quantity in an equation . In the case of algebraic expressions or algebra, variables are employed specifically. X+9=4, for instance, is a linear equation in which x is a variable and 9 and 4 are constants.

The variable is a quantity that, depending on the mathematical operation, can be changed or is not fixed. In algebra, generally we use the terms ‘x’ and ‘y’ to express any unknown quantities in the equation . However, this is not a compulsory condition; instead of that we can use any alphabet.