Equations

Equations:

Before we learn about the types of equations,let us understand the meaning of Equations.An equation is a mathematical statement that asserts the equality of two expressions. Equations consist of the expressions that to be equal on opposite sides of an equal sign, as in

x + 3 = 5,

9 - y = 7.,

One use of equations is in mathematical identities, assertions that are true independent of the values of any variables contained within them. For example, for any given value of x it is true that

x (x-1) = x^2-x\,.

However, equations can also be correct for only certain values of the variables. In this case, they can be solved to find the values that satisfy the equality. For example, consider the following.

x^2-x = 0\,.

The equation is true only for two values of x, the solutions of the equation. In this case, the solutions are x = 0 and x = 1.

Many mathmaticians reserve the term equation exclusively for the second type, to signify an equality which is not an identity. The distinction between the two concepts can be subtle; for example,

(x + 1)^2 = x^2 + 2x + 1,

is an identity, while

(x + 1)^2 = 2x^2 + x + 1,

is an equation with solutions x = 0 and x = 1. Whether a statement is meant to be an identity or an equation can usually be determined from its context. In some cases, a distinction is made between the equality sign ( = ) for an equation and the equivalence symbol (\equiv) for an identity.

Hope you like the above example of Equations.Please leave your comments, if you have any doubts.