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How do you know when an equation has infinitely many solutions?

When trying to solve an equation and you end up with the exact same number on both sides , like 10=10 then the equation has infinitely many solutions. If you end up with 2 different number on both side of the equation, like 3=5 then the equation has no solution. If there is a variable on one side and a number on the other, then there is one solution, e.g. x=4. In the equation 10=10 there is no variable such as x or y that we are trying to find the solution for. The equation x=x might be said to have an infinite number of solutions, because you can choose any value you like for x. More often you would say that "x is indeterminate". So if your equation always turns out to be satisfied for any x you choose, then there is an infinity of solutions and the equation does not represent anything useful. Or, for example, it may have a result such as "true for all even numbers", and you may not be aware in advance that this might happen. Or another example might be sin(x)=0 which has solutions for all values for those x which are integer multiples of 180 degrees. The only way is to solve the equation and see what appears.


What is 1 to the power of anything?

One to the power of anything is always one.


What is linear algebra used for?

Linear algebra is used to analyze systems of linear equations. Oftentimes, these systems of linear equations are very large, making up many, many equations and are many dimensions large. While students should never have to expect with anything larger than 5 dimensions (R5 space), in real life, you might be dealing with problems which have 20 dimensions to them (such as in economics, where there are many variables). Linear algebra answers many questions. Some of these questions are: How many free variables do I have in a system of equations? What are the solutions to a system of equations? If there are an infinite number of solutions, how many dimensions do the solutions span? What is the kernel space or null space of a system of equations (under what conditions can a non-trivial solution to the system be zero?) Linear algebra is also immensely valuable when continuing into more advanced math topics, as you reuse many of the basic principals, such as subspaces, basis, eigenvalues and not to mention a greatly increased ability to understand a system of equations.


What is the value of minus of any number to the power of zero?

Any number (except zero) to the zero power is 1. -1 If it was positive anything it would be 1. Anything positive to the power -0 = 1 Anything negative to the power -0 = -1


What does middle point of anything called?

The midpoint.

Related Questions

What is intellectual health?

An intellectual activity appeals to the intellect or the mind as opposed to the emotions. Intellectual activities might include reading, debating, analyzing, and brainstorming complex concepts, more for the stimulation it brings to the mind than anything else.


If brainstorming does not lead you to a strong idea what shouldn't you do?

If brainstorming doesn't do anything, maybe you need to think of another idea entirely - maybe your brain is trying to tell you that you don't want to work on that particular story at this time.


Which of the numbers below are solutions to the equation x2 equals -36?

38


What does Cyprus Solutions sell?

Cyprus Solutions is not a business so it does not sell anything. Cyprus Solutions is a term commonly referred to when talking about fixing problems in Cyprus.


What solutions in which water is the solvent are called?

Aqueous solutions are solutions in which water is the solvent. Anything that dissolves in water forms an aqueous solution.


What is web solutions and what do they do?

Web solutions refer to anything that helps business flourish online. It includes website design and management, online sales management, and online advertising.


Are mixtures and solutions similar?

Mixtures and Solutions are the same because they both use each other to do what they do. Solutions use Mixtures because you have to mix things together that are solutions to get solutions. Although mixtures don't need solutions to do anything solutions are very helpful.


What solutions can be used for air pollution?

try not to use your car as much or anything that pollutes the air = simple


What does 4x plus 7 equal to?

x can be anything, if you don't have it in an equation form, can an be an infinite amount of solutions


What is a potential roadblock?

A potential roadblock is an obstacle or barrier that may hinder progress, development, or success in achieving a specific goal or objective. It can be anything that stands in the way of smooth and efficient progress towards a desired outcome. Identifying and addressing potential roadblocks early on can help mitigate their impact and find solutions to overcome them.


How can analyzing the elements of fiction help readers understasnd the story more deeply?

Analyzing anything helps you to understand it better by helping you identify the parts and how they work together. Knowing what each part of the story is doing helps you understand the entire story better.


What are some security solutions on a laptop?

Security solutions on a laptop include using a linux based operating system instead of Windows, having a virus checker in place and not downloading anything from the Internet.