Nonlinear Systems of Equations Question

In summary, the conversation is about a person seeking help with a non-linear systems problem involving two functions, x^3 and x, and finding the points of interception. After attempting to factor the equation x-x^3=0, the person is unsure of how to proceed and is reminded to take out the common factor of x to get the solution. They thank the expert for their help.
  • #1
101
0
Ive been working on a bunch of non linear systems problems for homework and can't figure this one out:

y=xcubed
x-y=0

I get to the substitution stage and get x-xcubed=0, but you can't factor that so I am wondering what you do next to get the answers for x, and y.

Thanks in advance for any help
 
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  • #2
Are you sure you can't factor that? Can you factor out an x?
 
  • #3
if it can be factored i don't know how to do it lol
 
  • #4
These are two functions: f(x) = x^3 and g(x) = x. You have to find the points of interception, i.e. the points x for which f(x) = g(x).
 
  • #5
i appologize but i don't understand what your talking about
 
  • #6
Nevermind. Well, you said:

DethRose said:
I get to the substitution stage and get x-xcubed=0, but you can't factor that so I am wondering what you do next to get the answers for x, and y.

x - x^3 = 0 => x (1 - x^2) = 0.

I assume you'll know how to solve this problem now.
 
  • #7
ahh! i got you i feel like an idiot lol. I havnt done factoring for a while and I thought if you take the x out you get x-x^2 still

thanks for the help
 

1. What is a nonlinear system of equations?

A nonlinear system of equations is a system of equations where the variables are raised to powers other than 1 and are multiplied or divided together. This creates a curve when graphed rather than a straight line.

2. How is a nonlinear system of equations solved?

Unlike linear systems, there is no one specific method for solving nonlinear systems of equations. However, some common methods include substitution, elimination, and graphing. Additionally, numerical methods such as the Newton-Raphson method can also be used.

3. Can a nonlinear system of equations have multiple solutions?

Yes, a nonlinear system of equations can have multiple solutions. This is because the graph of a nonlinear system can intersect in multiple points, whereas a linear system can only have one solution.

4. What is the importance of studying nonlinear systems of equations?

Nonlinear systems of equations are important in many fields of science, including physics, engineering, and economics. They allow for more accurate modeling of real-world situations and can provide more complex and interesting solutions than linear systems.

5. What are some real-life examples of nonlinear systems of equations?

Real-life examples of nonlinear systems of equations include population growth, chemical reactions, and pendulum motion. These systems cannot be accurately modeled using linear equations and require the use of nonlinear systems to accurately predict outcomes.

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