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What is the difference b/w an equation and an identity?

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naveenks7 | Student, Undergraduate | eNotes Newbie

Posted April 2, 2009 at 9:48 PM via web

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What is the difference b/w an equation and an identity?

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deviselva75 | College Teacher | eNotes Newbie

Posted April 4, 2009 at 3:29 PM (Answer #1)

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An arithmetic expression that equates one set of conditions to another; for example, A = B + C.

identity :it is defined as an equality that holds regardless of the values of its variables

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted October 5, 2013 at 7:04 AM (Answer #2)

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The identity is a mathematical expression that is valid for all values of variables, while the equation is a mathematical expression that is valid only for certain values of variables.

Consider as example the following identity, such that:

`x^2 - y^2 = (x - y)(x + y)`

You should notice that the identity above holds for all real values of variables x and y.

Consider as example the following equation:

`xy - (x + y) + 1 = 0`

You need to notice that the identity `xy - (x + y) + 1 = 0` becomes valid only for `x = y = 1` , other real values of x and y being rejected.

Hence, you may say that the expression `xy - (x + y) + 1 = 0` represents an equation whose solutions are `x = y = 1.`

Hence, equation is a mathematical sentence that is used to evaluate the values of a variable, while the identity, is a mathematical sentence that is used to emphasize the equivalence of two mathmatical expressions.

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