Basics About Variables

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Variables are symbols or alphabets used in algebra that can be assigned different values. For example: when we write 2x^2 + 3y, here x and y are the variables, where as 2 and 3 are constants. These constants and variables together make up an algebraic expression.
To understand what are variables lets look at the following situation. Number of chocolates to be given to each child in a class is 3. Therefore number of chocolates for x children would be = 3x. Here x is a variable that can assume any value. (depending on the number of children in a particular class).

Types of variables:

Primarily there are two types of variables, the dependent variable and the independent variable. When the value of one variable depends on the value of another variable, then the first variable is called the dependent variable and the second variable is called the independent variable. For example, if y = 2x+3, then here x is the independent variable and y is the dependent variable. In z = x^2 + y^2, x and y are independent variables and z is the dependent variable because value of z depends on values of x and y.

Multiplying ...
... variables:

Since variables do not have a specific value, when we multiply variables of same type, we simply raise its power. For example, x * x = x^2, x^2 * x^3 = x^5 and so on. When we multiply variables of different types, we just write them together. For example, x * y =xy or x * z^2 = xz^2 or x * y * z = xyz.

Solving for variables:

Consider the same situation that we saw before. Number of chocolates to be given to each child in a class is 3. If y is the total number of chocolates required, then we can say that y = 3x. Now if we knew the total number of chocolates available, and we needed to find how many children would get 3 chocolates each, than what could be done? Suppose total number of chocolates = 90. Therefore y = 90, so our above equation now becomes 90 = 3x. So now if we were to find x, then we would get 90/3 = x => x = 30. So now we have solved the equation for x. If we were not given the specific value of y, then our solution for x would be x= y/3. So now y has become the independent variable and x has become the dependent variable.

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