Nonlinear Equation Algorithms

Nonlinear equation is the form of the multi variable equations and functions. In the equation there will be having more number of terms available. In the nonlinear equations the variables are not dependent to each other in the equation. Nonlinear equation has the more number of different orders of degrees. The graph of the nonlinear equation is not a straight line. It includes the quadratic function of equation and cubic function of equation. Here we are showing about the nonlinear equation algorithms and example problems in it .




Step by step algorithm for solving nonlinear equation:

Nonlinear equation algorithms:

Find whether the given equation is linear or nonlinear.

If the equation is equal to y = m x + b then the equation is linear equation
If the equation is not equal to y = mx + b then the given equation is nonlinear equation.

Find the equations of the order equal to any one of their variable and substitute the value in another equation.
Calculate the value for that equation and find two values.
Substitute the two values of the first equation in the second equation
Now we get each variable having two values.


Nonlinear equation algorithms - Example Problems:

Nonlinear equation algorithms - Problem 1:

Solve the nonlinear equations and find the value of x and y.

x2 - 8y = - 32

- x + y = 4

Solution:

Given equations

x2 - 8y = - 32   ------> Equation 1

- x + y = 4         ------> Equation 2

From the equation 2 rearrange and equal to y

y = 4 + x

Substitute the y value in the equation 1

x2 - 8(4 + x) = - 32

x2 - 32 -8x = -32

x2 - 8x -32+32 = 0

x2 -8x = 0

Solve the above equation by using factorization, we get

x(x - 8) = 0

Therefore the x value will be,

x=0            x - 8 = 0

x = 0 and x = 8

Substitute the x values in equation 2, we get

For x = 0,

y = 4 -x

y = 4 - 0

y = 4

For x = 8

y = 4 - 8

y = - 4

The value of y is 4, - 4


Nonlinear equation algorithms - Practice Problems:

1, Solve the nonlinear equations and find the value of x and y.

x2 - 7y = - 31

- x + y = 3

Answer:

x = 2 , 5 and y = 5, 8

2.

Find the nonlinear equations and find the value of x and y.

x = 2y - 3

y2 + 3x = - 2

Answer:

x = - 1, - 17 and y = 1, - 7