Difference Between Linear and Nonlinear Equations

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

We come across a lot of equations while solving maths problems. Some equations consist of 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.

Linear means something related to a line. All the linear equations are used to define or 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 difference between linear and nonlinear equations is explained here, for classes which have Maths chapters including topics of linear and nonlinear equations in a detailed manner. Students can easily understand these concepts and use them as a reference while solving maths problems.

Linear and Nonlinear Equations Differences

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 form a curve.
It has only one degree. Or we can also define it as an equation having the maximum order of 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 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.

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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