# Difference Between Linear and Non-Linear Equations

• Last Updated : 03 Jan, 2021

While solving mathematical problems, you may have seen types of equations. Few Equations can contain only numbers, others consist of only variables while some consists of both numbers and variables.

Linear and nonlinear equations usually consist of numbers as well as variables.

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Before starting with the difference between linear and non-linear equations, let us first understand the definition of Linear and Non-Linear Equation.

Linear Equation: A linear equation is such which forms a straight line. Linear means something related to a line. All the linear equations are used to construct a line. Linear Equations are conditions of the principal request. These conditions are characterized by lines in the arranged framework. An equation for a straight line is known as a Linear equation. The overall portrayal of the straight-line condition is y=mx+b, where m is the slant of the line and b is the y-catch.

Non-Linear Equations: 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. A non-linear equation is generally given by ax2+by2 = c

where x and y are variables

a,b and c are constant values.

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.

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.

### Sample Problems on Linear and Non-linear Equations

Problem 1: Solve the linear equation 3x+18 = 2x + 21.

Solution:

Given, 3x+18 = 2x + 21

⇒ 3x – 2x = 21 – 18

⇒ x = 3

Problem 2: Solve x = 12(x +2)

Solution:

x  = 12(x  + 2)

x = 12x + 24

Subtract 24 from each side

x – 24 = 12x + 24 – 24

x – 24 = 12x

Simplify

11x  = -24

Isolate x, by dividing each side by 11

11x / 11 = -24/11

x = -24/11

Problem 3: Solve the nonlinear equation x+4y = 1 and x = y.

Solution:

Given, x+4y = 1

x = y

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

⇒ y + 4y = 1

⇒ 4y = 1

⇒ y = 1/4

∴ x = y = 1/4

Problem 4: Example: Solve the nonlinear equation x+2y = 1 and x = 2

Solution:

Given, x+2y = 1

x = 2

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

⇒ 2+ 2y = 1

⇒ 2y = -1

⇒ y = -1/2

∴ y=-1/2

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