We have learned about equations in the earlier classes. An equation is a statement of the equality of two expressions. The two sides of the equality sign are referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation.
For example, in the equation 3x + 4 = 8, where 3, 4, and 8 are the constants, and x is the variable. The LHS is given by the expression 3x + 4 and the RHS is given by the constant 8. The equation remains unchanged if we carry out the same operation on both sides of the equation.
To solve an equation, we carry out a series of identical Mathematical operations on two sides of the equation such that the unknown variable is on one side and its value is obtained on the other side.
Equation: An equation is a statement of equality of two algebraic expressions involving constants and variables.
Based on the degree and variable in the equations, they are classified as linear and nonlinear equations.
Linear Equation
An equation in which the maximum degree of a term is one is called a linear equation. Or we can say that a linear equation that has only one variable is called a linear equation in one variable.
A linear equation value when plotted on the graph forms a straight line.
The general form of a linear equation is ax + b = c, where a, b, c are constants and a0 and x and y are variables.
For Example: x + 7 = 12, 5/2x – 9 = 1, x2 + 1 = 5 and x/3 + 5 = x/2 – 3 are equations in one variable x.
Here the highest power of each equation is one.
2x + 3y = 15, 7x – y/3 = 3 are equations in two variables x and y.
When the linear equation is plotted on the graph we get the below figure.
Nonlinear Equation
An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation.
For example [3x^{2}] + 2x + 1 = 0, 3x + 4y = 5, this is the example of nonlinear equations, because equation 1 has the highest degree of 2 and the second equation has variables x and y.
The nonlinear equation values when plotted on the graph forms a curve.
The general form of a nonlinear equation is [ax^{2} + by^{2} = c], where a, b, c are constants and a0 and x and y are variables.
When plotted on the graph we get the below curve
Difference Between Linear and Nonlinear Equations
Understanding the difference between linear and nonlinear equations is foremost important. Here is the table which will clarify the difference between linear and nonlinear equations. So let us understand exactly what linear and nonlinear equations are.
Differentiate Between Linear and Nonlinear Equations
|
Linear Equations |
Non-Linear Equations |
|
A Linear equation can be defined as the equation having a maximum of only one degree. |
A Nonlinear equation can be defined as the equation having the maximum degree 2 or more than 2. |
|
A linear equation forms a straight line on the graph. |
A nonlinear equation forms a curve on the graph. |
|
The general form of linear equation is, y = mx +c Where x and y are the variables, m is the slope of the line and c is a constant value. |
The general form of nonlinear equations is, ax2 + by2 = c Where x and y are the variables and a,b and c are the constant values |
|
Examples: |
Examples:
|
Let us understand what are linear and nonlinear equations with the help of some examples.
Solved Examples
Example1: Solve the Linear equation 9(x + 1) = 2(3x + 8)
Solution:
9(x + 1) = 2(3x + 8)
Expand each side
9x + 9 = 6x + 16
Subtract 6x from both the sides
9x + 9 – 6x = 6x + 16 – 6x
3x + 9 = 16
Subtract 9 from both the sides
3x + 9 – 9 = 16 – 9
3x = 7
Divide each by 3
3x/3 = 7/3
x= 7/3
Example 2 : Solve the nonlinear equation
[3x^{2}] – 5x + 2 = 0
Solution:
[3x^{2}] – 5x + 2 = 0
Factorizing
[3x^{2}] – 3x – 2x + 2 = 0
3x(x – 1) – 2(x – 1) = 0
( 3x – 2)( x – 1) = 0
(3x – 2) = 0 or (x – 1) = 0
x = 2/3 or x = 1
Quiz Time
Q. Solve the following linear equation and find the value of x
-
3(5x + 6) = 3x – 2
-
(2x +9)/5 = 5
Q. Solve the nonlinear equations
-
[7x^{2} = 8 – 10x]
-
[3x^{2} – 4 = 5x]
Knowing basic math is important not only in each of the standards but it is also important that you keep your foundation strong even when you are learning for any higher class Math. Now finding these concepts online is not a problem at all as you can find them all listed on . Here you will get to know what is the Difference Between Linear and Nonlinear Equations and how to distinguish between them! Learning the concepts related to the linear equation and non-linear equation will help you solve a lot of problems in Algebra as well.
What Forms A Linear Equation?
The simplest form of a linear equation can be explained in the form y = a + bx where both a and b represent constants in an equation while there will be two variables that will be present. This forms the backbone of the linear equation. This linear equation when it is plotted on a graph paper will yield you a straight line with the line passing through the origin. It will have a constant slope value throughout the straight line that is passing through the origin.
Distinguish Between Linear and Non-Linear in A Single Look
When talking about linear and nonlinear equations it is to be understood that the linear equations will have no exponents while the non-linear equations that are present will contain exponents raised to higher powers than 1.