The table given below will help us to find the number of solutions to a linear equation in one variable. Example 1 :. Solution :. Subtract 2x from each side. Divide each side by 2. Justify and Evaluate :. Example 2 :. When we solve the given equation, we don't find 'x' in the result. So there are infinitely many solutions.

Example 3 :. When we solve the given equation, we don't find "x" in the result. So, there is no solution. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. You can also visit our following web pages on different stuff in math. Variables and constants. Writing and evaluating expressions. Solving linear equations using elimination method.

Solving linear equations using substitution method. Solving linear equations using cross multiplication method. Solving one step equations. Solving quadratic equations by factoring. Solving quadratic equations by quadratic formula. Solving quadratic equations by completing square.

### No solutions, one solution, infinitely many solutions?

Nature of the roots of a quadratic equations. Sum and product of the roots of a quadratic equations.This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. Learn more Accept. System of Equations. Conic Sections Trigonometry. Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties.

System of Equations Calculator Solve system of equations step-by-step. Correct Answer :. Let's Try Again :. Try to further simplify. Solving simultaneous equations is one small algebra step further on from simple equations. Symbolab math solutions A system of equations is a collection of two or more equations with the same set of variables. In this blog post, Sign In Sign in with Office Sign in with Facebook. Join million happy users! Sign Up free of charge:.

Join with Office Join with Facebook. Create my account. Transaction Failed! Please try again using a different payment method. Subscribe to get much more:.Subtracting 7 x from both sides. Hence, the given linear equation has zero solution or the number of solutions is zero. Hence, the given linear equation has no solution or the number of solutions is zero. Hence the given linear equation has Infinite solutions or the number of solutions is infinite.

Subtracting 15 x from both sides. From the above examples we can say that, the linear equation will have infinite solutions if it is satisfied by any value of the variable or every value of the variable makes the given equation a true statement. Email Us. Research has proven that personal online tutoring not just cements school learning, it helps build student confidence.

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Sign up for a Free Trial Lesson Today! Thousands have taken the eTutorWorld Advantage — what are you waiting for? Linear equations with one, zero, or infinite solutions.

Here we will try to find out the number of possible solutions of any linear equation. Now we consider each of the above cases separately and understand them with examples. Linear Equations With one Solution. Linear equations with infinite solutions. Answer key One Solution i. Infinite Solutions. Zero Solution. One Solution i. Quick Links. Follow Us. Give Your Child The eTutorWorld Advantage Research has proven that personal online tutoring not just cements school learning, it helps build student confidence.

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Thread starter frctl Start date Aug 28, Joined Jun 29, Messages Under what conditions on a and b will the following linear system have no solutions, one solution, infinitely many solutions? Peterson Elite Member. Joined Nov 12, Messages 6, What thoughts do you have about it? What would you look for to answer a question like this, if I gave you specific values for a and b? One thing to consider is what the slopes of the two lines will be.

It appears the second eqn is twice the first. Joined Mar 25, Messages 1, Joined Mar 16, Messages 1, No solution means the lines will be parallel. Infinite solutions means the lines are the exact same lines. If they're not the same line and are not parallel then they must intersect in one point. So under what condition for a and b, will each of those three cases hold? I can't find anything for these two equations. Well, you're getting closer, but again I ask "Are you sure about that?

Are they the same line? It may help you figure out the proper conditions for the lines to be the same line if you think in terms of the equations.

I'll give three examples of a pair of lines. Exactly one of these pairs is actually the same line. Can you identify which one?By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. So I've forgotten what the conditions for when a matrix has zero, one and infinitely many solutions. Sign up to join this community. The best answers are voted up and rise to the top.

Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown.Finding examples of linear equations in one variable with one, none, or many solutions 8. Show Step-by-step Solutions Solving Equations with different types of solutions. Show Step-by-step Solutions Number of solutions to linear equations. Show Step-by-step Solutions Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. We welcome your feedback, comments and questions about this site or page.

Please submit your feedback or enquiries via our Feedback page. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Common Core: 8. The following table shows examples of linear equations in one variable with one, none, or many solutions. Scroll down the page for more examples and solutions. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.Inf is a calculator that can handle infinite and infinitesimal numbers.

Type an expression at the : prompt and hit Enter. For more documentation, scroll down. Inf represents infinite and infinitesimal quantities as Levi-Civita numbers. Calculus students often get the impression that the notion of an infinite or infinitesimal number can never be defined in any rigorous or self-consistent way.

That's not true. Tullio Levi-Civita defined the Levi-Civita numbers aroundso it's been known for over a century that there were rigorously definable number systems that included infinities. Great mathematicians like Newton, Gauss, and Euler used infinitesimals, and now that modern mathematicians have put them on a more rigorous footing, there's no reason to shy away from them. To learn more about the application of infinitesimals to calculus, see my free calculus book.

If you've ended up here because the calculus book tells you about the calculator, one thing you should realize is that the Levi-Civita numbers used by Inf are not the full hyperreal number system referred to in the book. They are a subset of them, in the same way that the rational numbers are a subset of the real numbers. This is why certain calculations give an error in the calculator, even though they are well defined in the hyperreals.

This is because one of the elementary axioms of arithmetic is that division by zero is undefined. To see why there have to be many different sizes of infinities, and of infinitesimals, consider the following example.

Augmented Matrices with 0, 1 or Infinite Solutions 141-44

We can prove from the elementary axioms of arithmetic is that if x is greater than zero, then 2x is greater than x. This applies to Levi-Civita numbers as well, so infinite and infinitesimal numbers have to come in different sizes. This shows that the traditional practice of neglecting the square of an infinitesimal can't be formalized in the Levi-Civita system simply by equating it to zero. We can, however, say that neglecting a d 2 term compared to a d is an infinitely good approximation.

To amplify on statement 2 above, the infinitesimal d doesn't have any special properties that would allow it to be picked out from among all the other positive infinitesimals. We just assume it can be picked arbitrarily from the set of positive infinitesimals. The arbitrariness of this choice can be understood by analogy with the complex numbers.

It follows from the axioms of algebra that there are two such solutions with opposite signs, since the sign of x doesn't affect the value of x 2. We call one of these i, and the other -i. Note that it makes absolutely no difference which one is i and which is -i.

## EQUATIONS WITH MANY SOLUTIONS OR NO SOLUTION

The hyperreals match the properties of the real numbers even better than the Levi-Civita numbers do. For example, the exponential function can take a positive infinite argument in the hyperreal system, but that doesn't work in the Levi-Civita numbers.

However, the hyperreals cannot be conveniently represented on a computer. In Firefox, you can use up-arrow and down-arrow to get back lines you've typed in previously. Depending on your browser, it may also be possible to accomplish this using control-P and control-N.

Inf is open source software by Ben Crowell and Mustafa Khafateh. It's under the GPL v.

### Solving system of linear equations

Since it's all written in client-side javascript, you can see the source code simply by doing "view source" in your browser; actually most of the code is in separate modules pointed to from the html source code, but you can view those through your browser as well by pointing it at each URL. Alternatively, you can access it via a web browser or git, at via github.

About Inf Basic use Inf is a calculator that can handle infinite and infinitesimal numbers. Built-in functions: sin, cos, tan asin, acos, atan sqrt, abs exp, ln Inf represents infinite and infinitesimal quantities as Levi-Civita numbers.

There are two basic things to understand about this system: The Levi-Civita numbers obey all the same elementary axioms of arithmetic as the real numbers. The system contains many different sizes of infinite numbers, and many sizes of infinitesimals, but all of them are expressed in terms of the basic building block d, which is a positive infinitesimal that we arbitrarily single out and give a name.