# What Is an Equation?

An equation is a relationship between two things (often numbers and/or symbols) that are equal to one another.

Equality is denoted by the equals sign =.

# Examples of Equations

It is obvious that a thing must be equal to itself:

Sometimes this may be expressed less obviously. Here, both side evaluate to 2:

Symbols and letters can be introduced as well as numbers:

In this case, both sides are only equal when x = 2, because 2 + 3 = 5. x = 2 solves the equation.

(Note: This is an algebraic equation and can be solved using algebra).

# Some Important Types of Equations

Many equation are functions. They relate an input (x) to an output (y).

Some important equations are:

• Linear Equations

A linear equation looks like:

Here, x = 1 and y = 3 will make both sides equal and so solve the equation.

So will x = 2 and y = 4, or x = 3 and y = 5; in fact an infinite number of pairs of x and y will solve the equation.

(Note: If the pairs of x and y that solve the equation are plotted on a graph, it will make a line.)

Here, x = 1 and y = 3 will make both sides equal and so solve the equation.

So will x = 2 and y = 6, or x = 3 and y = 11; in fact an infinite number of pairs of x and y will solve the equation.

(Note: If the pairs of x and y that solve the equation are plotted on a graph, it will make a curve.)

# The Parts of an Equation

Below is an equation. It is an equation because it has an equals sign.

Each number or symbol (or number multiplied by a symbol) is a term. The terms are separated by operators, such as a + or -.

When the terms are grouped together with operators, they form an expression.
Algebra Lessons
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##### Note
THE = SIGN

The first recorded use of the equals sign = in an equation (as well as the plus + and minus - signs in an English book) was by Robert Recorde (1510 - 1558).

The first equation appears in his book 'The Whetstone of Witte':

It is equivalent to '14x + 15 = 71' in today's notation. He chose two parallel lines of equal length, "bicause noe 2 thynges can be moare equalle."

UNKNOWNS, CONSTANTS AND CO-EFFICIENTS

Equations have unknowns, constants and co-efficients.

Unknowns are the variables that take different values. They are denoted by letters: x, y and z.

Constants take just one number, lke 2 or -4. They too are sometimes denoted by letters: a, b and c.

Co-efficients can also take just one number, but they are multiplying the unknowns. They can be denoted by the same letters as constants are. For example, in the term 4x, 4 is the co-efficient of x. It means x is multiplied by 4.