# Solving System of Equations - Critical Points

• CoolDude420
In summary, the conversation revolves around finding critical points for a 3 variable function by solving a system of 3 equations. The person is struggling with this task and has encountered some mistakes in their working, which they are in the process of correcting. The goal is to find the critical points in order to use the second derivative test to determine their type.
CoolDude420

## Homework Statement

[/B]
Hi,
I seem to have this issue with solving the a system of 3 equations when trying to find the critical points for a 3 variable function.

## The Attempt at a Solution

It always keeps happening. I keep getting stuck when solving these equations. Every single question has its own little trick in it on how to solve these equations

Any ideas? I need to do this as the first part in solving my question. I need to find the critical points then use the second derivative test to determine the type of critical points. I keep going around and around with equations, trying to fit them into other ones and it leads me nowhere.

why is it that in your working
yz = 1/(2 x^2) becomes y = z/(2 x^2)
similarly
xz = 1 /(y^2) becomes x=z/(y^2)
and
xy=2/z^2 becomes x = 2y/z^2

it it that i am missing something or is it did you make a mistake?

vishnu 73 said:
why is it that in your working
yz = 1/(2 x^2) becomes y = z/(2 x^2)
similarly
xz = 1 /(y^2) becomes x=z/(y^2)
and
xy=2/z^2 becomes x = 2y/z^2

it it that i am missing something or is it did you make a mistake?

They are all mistakes.

Ray Vickson said:
They are all mistakes.
Oops. seems like i forgot some basic algebra. Give me a second ill fix that up.

## 1. What is a critical point in a system of equations?

A critical point in a system of equations is a solution where all the variables are equal to zero. In other words, it is the point where the equations intersect and have a common solution.

## 2. How do you solve a system of equations to find critical points?

To solve a system of equations and find critical points, you can use a variety of methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to eliminate variables and find the common solution.

## 3. Why are critical points important in solving systems of equations?

Critical points are important because they represent the points where the equations have a common solution. These points provide valuable information about the behavior of the system and can help in finding the optimal solution.

## 4. Are there any limitations in using critical points to solve systems of equations?

One limitation of using critical points is that they may not always exist for every system of equations. In some cases, the equations may have no common solution or may have an infinite number of solutions, making it difficult to find the critical points.

## 5. How can critical points be applied in real-life situations?

Critical points can be applied in various real-life situations such as optimization problems, where the goal is to find the maximum or minimum value of a function. They can also be used in economics, physics, and engineering to analyze the behavior of systems and make predictions.

• Calculus and Beyond Homework Help
Replies
27
Views
639
• Calculus and Beyond Homework Help
Replies
1
Views
393
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
2K
• Calculus and Beyond Homework Help
Replies
10
Views
681
• Calculus and Beyond Homework Help
Replies
3
Views
486
• Calculus and Beyond Homework Help
Replies
2
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
12
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
1K