# What is the difference between an algebraic expression and an algebraic equation? Give some...

## Question:

What is the difference between an algebraic expression and an algebraic equation?

Give some examples.

Give an example of an equation used in a real life scenario

## Algebraic expression:

An algebraic expression is an expression involving the terms with variables like x, y, z etc and basic mathematical operations like addition, subtraction, multiplication and division. For example, {eq}(2x+3y-4z+7)\ {/eq}is an algebraic expression in variables x, y, z, where the operations are addition and subtraction.

## Algebraic equation:

An algebraic equation is an equality where an algebraic expression written in the left hand side is equated with another expression or constant written in the right hand side.

For example, {eq}x-8y-5z+t=9\ {/eq}is an algebraic equation in variables x,y,z and t.

## Answer and Explanation:

For an example if we consider the real life scenario:

The cost of 2 pens and 3 pencils is 7 dollars and the cost of 5 pens and 2 pencils is 12 dollars. Find the cost of one pen and one pencil.

Here, we assume the cost of 1 pen is x dollars and the cost of 1 pencil is y dollars.

Then we get two equations in variables x, y as follows:

{eq}2x+3y=7............. (1)\\ 5x+2y=12............(2) {/eq}

Solving these equations we can find the cost of 1 pen is 2 dollars and the cost of 1 pencil is 1 dollar.