# Nonlinear Equations

## Definition of Non-linear equations

The nonlinear equations are those equations that do not form a straight line when plotted. Rather, nonlinear equations form a curve.

In other words, non-linear equations are the equations obtained by equating polynomials of degree 2 or more to zero.

## General representation of non-linear equations

The general representation of nonlinear equations is as follows:

$a{x^2} + b{y^2} = c$

## Examples of Nonlinear equations

1. ${x^2} + {y^2} = 4$
2. $2{x^2} + 3xy + {y^2} = 8$
3. ${x^2} + 2xy = 5$

What is nonlinear equation?

The nonlinear equations are the equations which forms a curve when plotted. The nonlinear equations are of degree 2 or more than 2.

What is a nonlinear equation example?

The example of a nonlinear equation is the equation of a circle: ${x^2} + {y^2} = {r^2}$. Where, r is the radius of the circle.

How do you know if a equation is nonlinear?

A nonlinear equation can easily be found out by checking the degree of the equation. A nonlinear equation has a degree of 2 or more than 2. Also, when nonlinear equations are plotted in x-y cartesian coordinate system it forms a curve.

How do you write a nonlinear equation?

A nonlinear equation having degree 2 can be written in the following form: $a{x^2} + b{y^2} = c$

How do you graph a nonlinear equation?

The nonlinear equations can be plotted in the graph by putting the values of x and y in the x-y cartesian coordinate system.
Let a non linear equation be: ${x^2} + y = 2$
$\therefore y = 2 - {x^2}$
When, $x = 1,\,\,\,y = 2 - 1 = 1$
$x = 2,\,\,y = 2 - 4 = - 2$
$x = 3,\,\,y = 2 - 9 = - 7$
If we plot the above values in the x-y cartesian system the graph will be as shown in the figure.

How do you solve a nonlinear algebraic expression?

To solve a nonlinear algebraic expression of degree 2, let us consider the algebraic expression as
${x^2} + y = 2$
$\therefore y = 2 - {x^2}$
When, $x = 1,\,\,\,y = 2 - 1 = 1$
$x = 2,\,\,y = 2 - 4 = - 2$
$x = 3,\,\,y = 2 - 9 = - 7$

What makes an equation linear?

The linear equation when plotted in the x-y cartesian coordinate system always forms a straight line.

What is an example of nonlinear function in real life?

Driving a car is an example of nonlinear function in real life. While driving a car, the speed of the car is not constant and changes over time. At high traffic areas the speed of the car reduces and at low traffic areas the speed of the car increases. Therefore, driving a car is nonlinear.

What are the differences between linear and nonlinear equations?

The main difference between linear and nonlinear equations is that linear equation forms straight line when plotted whereas the nonlinear equations forms a curve. Also the linear equations have degree of 1 whereas the nonlinear equations have degree 2 or more than 2.