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What is the Meaning of Equation – Definition, Types & Examples

what is the meaning of equation

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Equations are used by many professionals like engineers, architects, video game designers, etc. For example, air traffic controllers frequently use equations to calculate the minimum safe level for planes to fly at. To do this they use the equation $\text{Minimum safe level (measured in feet)} = 30 \times\left (1013 – \text{ pa} \right)$, where $\text{pa}$ is the atmospheric pressure.  

The term equation can be defined in numerous ways. In its simplest form, we can say that an equation is a mathematical statement that shows that two algebraical expressions are equal.

Let’s understand what is the meaning of equation and what are its different types.

What is the Meaning of Equation?

You know that an algebraic expression is a mathematical statement consisting of constants, variables, and mathematical operators. Equations are mathematical statements containing two algebraic expressions on both sides of an ‘equal to ($=$)’ sign. 

The equation shows the relationship of equality between the expression written on the left side with the expression written on the right side. Mathematically, we say that for any equation L.H.S = R.H.S (left-hand side = right-hand side). 

The purpose of the equations is to find the value(s) of the unknown quantities or variables. The procedure of finding the value(s) of the unknowns in the equation is known as solving an equation. 

what is the meaning of equation

Writing an Equation

An equation is a statement consisting of two algebraic expressions connected by an equal sign (“=”). These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. 

In most cases, the right-hand side of the equation is zero(0). This will not reduce the generality since we can balance this by subtracting the right-hand side expression from both sides’ expressions.

what is the meaning of equation
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Maths can be really interesting for kids

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an ‘equal to ($=$)’ sign, and terms on both sides. Both sides should be equal to each other. 

An equation doesn’t need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, $2 + 3 = 5$. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation. 

These are the different parts of an equation.

what is the meaning of equation

What is the Degree of an Equation?

The highest power of a variable in the equation is called the degree of an equation.

For example in the equation $2x + 5 = 3$, there is only one variable and its power is $1$ ($x = x^{1}$), therefore, degree of $2x + 5 = 3$ is $1$.

For the equation $x – 3y = 7$, the degree is $1$, since both the variables have power $1$.

Similarly, for the equation $5x^{2} – 2x + 7 = 0$, the degree is $2$.

For the equation, $x – xy + y = 1$, the degree of equation is $2$, since, in $xy$, power of both $x$ and $y$ is $1$, therefore, power of $xy$ is $2\left(1 + 1 \right)$.

Types of Equation

Based on the degree, equations can be classified into three types. The different types of equations are: 

  • Linear Equations
  • Quadratic Equations
  • Cubic Equations
  • Higher Order Equations

Linear Equation

Equations with degree $1$ are known as linear equations in math. In such equations, $1$ is the highest exponent of terms. These can be further classified into linear equations in one variable, linear equations in two variables, linear equations in three variables, etc. 

The standard form of a linear equation in one variable is $ax + b = c$.

For example, in equation $2x + 3 = 7$, $a = 2$, $b = 3$ and $c = 7$.

The standard form of a linear equation in two variables is $ax + by = c$.

For example, in equation $5x – 2y = 8$, $a = 5$, $b = -2$ and $c = 8$. Similarly, for equation $7x + 3y – 9 = 0$, $a = 7$, $b = 3$ and $c = 9$, since the equation can also be written as $7x + 3y = 9$.

Quadratic Equation

Equations with degree $2$ are known as quadratic equations. The standard form of a quadratic equation with variable $x$ is $ax^{2} + bx + c = 0$, where $a \ne 0$. 

For example, $2x^{2} + 3x – 5 = 0$ is a quadratic equation or an equation of degree $2$ and here, $a = 2$, $b = 3$, and $c = -5$.

Cubic Equation

Equations with degree $3$ are known as cubic equations. Here, $3$ is the highest exponent of at least one of the terms. The standard form of a cubic equation with variable $x$ is $ax^{3} + bx^{2} + cx + d = 0$, where $a \ne 0$..

Example of a cubic equation is $8x^{3} – 2x^{2} + 6x – 12 = 0$.

Higher Order Equation

Equations with degrees greater than $3$ are known as higher-order equations. In all such equations, the highest exponent of at least one of the terms is greater than $3$. 

Examples of higher-order equations are

$x^{4} – 3x^{3} + x^{2} – 5x + 2$ ($4$-degree equation)

$2x^{5} + 7x^{4} + x^{3} – 8x^{2} + 6x – 10$ ($5$-degree equation)

Types of Coordinate Systems

Graph of an Equation

The graph of an equation can be obtained by plotting the points $\left(x, y \right)$ satisfying the equation in the Cartesian plane. The graph of a linear equation(equation of degree $1$) is a straight line, whereas the graph of quadratic, cubic, and higher-order equations are curves.

what is the meaning of equation

Difference Between an Algebraic Equation and an Algebraic Identity

Following are the differences between an algebraic equation and an algebraic identity.

what is the meaning of equation

Practice Problems

State True or False

  • The LHS and RHS of an equation are not always true.
  • For every equation, all values given to variable(s) make LHS equal to RHS.
  • An algebraic equation can have no variable.
  • An equation can have an inequality sign such as $\lt$, $\gt$, $\le$, or $\ge$.
  • An equation with degree $4$ is called a quadratic equation.
  • The degree of an equation is the highest number of variables in it.
  • All algebraic equations are algebraic identities.
  • All algebraic identities are algebraic equations.

FAQs

What is an equation in math?

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign. For example, $2m + 9 = 15$ is an equation.

What is a linear equation?

An equation with degree $1$ is called a linear equation. It means the highest exponent of any term could be $1$. An example of a linear equation in one variable is $7x + 12 = 17$ and a linear equation in two variables is $2x + 3y = 18$.

What is a quadratic equation?

An equation with degree $2$ is called a quadratic equation. It can have any number of variables but the highest power of terms could be only $2$. The standard form of a quadratic equation with variable $x$ is a$x^{2} + bx + c = 0$, where $a \ne 0$. For example $x^{2} – 6x + 8 = 0$ is a quadratic equation.

What are the parts of an equation?

what is the meaning of equation

The different parts of an equation are terms, coefficients, exponent, arithmetic operator, equal to sign, and constants.

Should the LHS and RHS of an equation be equal?

Yes, the LHS (left-hand side) and RHS (right-hand side) of an equation must be equal.

Conclusion

An equation shows the relationship of equality between the expression written on the left side with the expression written on the right side. In this article, we learned what is the meaning of an equation and its parts and also what are the different types of equations.

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