Sample Problems – Difference Between 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

Difference Between Linear and Non-Linear Equations: While solving mathematical problems, you may have seen types of equations. Few Equations can contain only numbers, others consist of only variables while some consist of both numbers and variables. Linear and nonlinear equations usually consist of numbers as well as variables.

In this article, we will understand the difference between Linear and Non-Linear Equations along with sample problems.