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What Is an Equation? (Mathematics Lesson)

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.)


  • Quadratic Equations

    A quadratic 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 = 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.
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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.