Difference Between Linear and Nonlinear Equations

In Mathematics, you must have learned about different types of equations. Here, we are going to discuss the difference between linear and nonlinear equations. The difference between them described here with the help of definitions and examples.

We come across a lot of equations while solving maths problems. Some equations include only numbers and some consist of only variables and some consists of both numbers and variables. Linear and nonlinear equations usually consist of numbers and variables. A variable is a quantity which could be any integer value.

Definition of Linear and Non-Linear Equation

Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.

The major difference between linear and nonlinear equations is given here for the students to understand it in a more natural way. The differences are provided in a tabular form with examples.

What is the difference between Linear and Nonlinear Equations?

To find the difference between the two equations, i.e. linear and nonlinear, one should know the definitions for them. So, let us define and see the difference between them.

Linear Equations

Non-Linear Equations

It forms a straight line or represents the equation for the straight line It does not form a straight line but forms a curve.
It has only one degree. Or we can also define it as an equation having the maximum degree 1. A nonlinear equation has the degree as 2 or more than 2, but not less than 2.
All these equations form a straight line in XY plane. These lines can be extended to any direction but in a straight form. It forms a curve and if we increase the value of the degree, the curvature of the graph increases.
The general representation 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 representation of nonlinear equations is;

ax2 + by2 = c

Where x and y are the variables and a,b and c are the constant values

Examples:

  • 10x = 1
  • 9y + x + 2 = 0
  • 4y = 3x
  • 99x + 12 = 23 y
Examples:

  • x2+y2 = 1
  • x2 + 12xy + y2 = 0
  • x2+x+2 = 25

Note:

The linear equation has only one variable usually and if any equation has two variables in it, then the equation is defined as a Linear equation in two variables. For example, 5x + 2 = 1 is Linear equation in one variable. But 5x + 2y = 1 is a Linear equation in two variables.

Let us see some examples based on these concepts.

Solved Examples

Example: Solve the linear equation 3x+9 = 2x + 18

Solution: Given, 3x+9 = 2x + 18

⇒ 3x – 2x = 18 – 9

⇒ x = 9

Example: Solve the nonlinear equation x+2y = 1 and x = y

Solution: Given, x+2y = 1

x = y

By putting the value of x in the first equation we get,

⇒ y + 2y = 1

⇒ 3y = 1

⇒ y = ⅓

∴ x = y = ⅓

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Frequently Asked Questions – FAQs

What is the key difference between non-linear and linear equations?

A linear equation is used to represent a straight line in a graph, whereas non-linear equations are used to represent curves and the changes or variation in the graph.

How does the graph of linear and non-linear equations look?

A linear equation graph is a constant slope whereas the graph of the non-linear equation shows he variation in slope at different points.

How is the linear equation represented? Give an example.

The general representation of linear equation is y = mx+c,
where m = slope of the line
x and y are the variables
c is the intercept (constant value)
Example: 2x+y=1
y=-2x+1

How is the nonlinear equation formed?

A non-linear equation is generally given by ax2+by2 = c
where x and y are variables
a,b and c are constant values.

1 Comment

  1. good explanation of difference between Linear and Nonlinear Equations

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