If you're seeing this message, it means we're having trouble loading external resources on our website. Show If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. An infinite solution is a mathematical statement that can be proven to be true, but that does not have a finite answer. This means that the statement can be proven to be true an infinite number of times, but that there is no specific number that can be assigned to it. Infinite solutions often arise in mathematics when dealing with infinity, as there are an infinite number of numbers in this set. 
Register to Get Free Mock Test and Study Material Grade Are you a Sri Chaitanya Student? +91 Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Conditions for Infinite Solution of a Linear Differential EquationA linear differential equation has a finite number of solutions if the coefficients of the equation are all finite. If one or more of the coefficients is infinite, then the equation may have an infinite number of solutions. To determine whether or not a linear differential equation has an infinite number of solutions, one must determine whether or not any of the coefficients are infinite. If any of the coefficients are infinite, then the equation has an infinite number of solutions. Infinite Solutions ExampleAn infinite solution is a mathematical solution that continues forever. There are many different types of infinite solutions, including infinite series, infinite products, and infinite quotients. Infinite solutions can be difficult to understand and even more difficult to calculate, but they can be extremely useful in solving mathematical problems. Approaching the Infinite Solution TopicThe infinite solution is the set of all real numbers. This set is uncountable, meaning that it cannot be put into a one-to-one correspondence with the natural numbers. In other words, there are infinitely many real numbers, and no finite number of them could ever represent them all. The infinite solution is often used in proofs involving the real numbers. For example, a proof might show that a certain equation has no solution in the natural numbers, but that it does have a solution in the infinite solution. Note: In order to solve the problem related to coordinate geometry students must not solve the problem mathematically but should also try to find out the physical meaning of the problem. Students must remember these conditions in order to solve such problems of coordinate geometry. Infinite solutions article is developed by the highly qualified teachers of Vedantu. These teachers have a good deal of experience in the field of education and are very well aware of the needs of the students. It is often seen, students are unable to comprehend the topic despite working hard over it. The reasons for the same could be the tough language of the content, lengthy and monotonous flow of the article and others. Whereas the Infinite Solutions - Definition, Conditions, and Examples article prepared by Vedantu takes care of these elements and tends to make the article more and more interesting for the students. Now learning and fun go hand in hand. We all are well acquainted with equations and expressions. We solve it almost daily in mathematics. Let's just quickly refresh the meanings of the terms once again before we dig in. An equation is an expression that has an equal sign (=) in between. For example, 4+3 = 7. An expression consists of variables like x or y and constant terms which are conjoined together using algebraic operators. For example, 2x + 4y - 9 where x and y are variables and 9 is a constant. As far as we look there is usually one solution to an equation. But it is not impossible that an equation cannot have more than one solution or an infinite number of solutions or no solutions at all. Having no solution means that an equation has no answer whereas infinite solutions of an equation mean that any value for the variable would make the equation true. What are Infinite Solutions?The total number of variables in an equation determines the number of solutions it will produce. And based on this, solutions can be grouped into three types, they are:
But how would you know if the solution to your solved equation is infinite? Well, there is a simple way to know if your solution is infinite. An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution. Infinite represents limitless or unboundedness. It is usually represented by the symbol ” ∞ “. Conditions for Infinite SolutionAn equation will produce an infinite solution if it satisfies some conditions for infinite solutions. An infinite solution can be produced if the lines are coincident and they must have the same y-intercept. The two lines having the same y-intercept and the slope, are the exact same line. In simpler words, we can say that if the two lines are sharing the same line, then the system would result in an infinite solution. Hence, a system will be consistent if the system of equations has an infinite number of solutions. For example, consider the following equations. y = x + 3 5y = 5x + 15 If we multiply 5 to equation 1, we will achieve equation 2 and by dividing equation 2 with 5, we will get the exact first equation. Infinite Solutions ExampleWhat is an example of an infinite solution? This is the question we were waiting for so long. But to solve systems of an equation in two or three variables, it is important to understand whether an equation is a dependent one or an independent one, whether it is a consistent equation or an inconsistent equation. A consistent pair of linear equations will always have unique or infinite solutions. Example 1: Here are two equations in two variables. a1x + b1y = c1 ——- (1) a2x + b2y = c2 ——- (2) If (a1/a2) = (b1/b2) = (c1/c2) Then the equation is a consistent and dependent equation that has infinitely many solutions. Example 2: Here are few equations with infinite solutions -6x + 4y = 2 3x - 2y = -1 Now if we multiply the second equation by -2, we will get the first equation. -2(3x-2y) = -2(-1) -6x + 4y = 2 Therefore, the equations are equivalent and will share the same graph. So, the solution that will work for one equation would also work for other equations as well. Hence, they are infinite solutions to the system. Example 3: x-10+x = 8+2x-18 Now, here is how we proceed x-10+x = 8+2x-18 2x-10 = 2x-10 -2x = -2x -10 = -10 Since -10 = -10 we are left with a true statement and we can say that it is an infinite solution. Example 4: Let us take another example: x+2x+3+3 = 3(x+2) x+2x+3+3 = 3(x+2) 3x+6 = 3x+6 -3x = -3x 6 = 6 The coefficients and the constants match after combining the like terms. This gives us a true statement. Therefore, there can be called infinite solutions. Example 5: Consider 4(x+1)=4x+4 as an equation. 4(x+1) = 4x+4 4x+4 = 4x+4 We can see that in the final equation, both sides are equal. Therefore, it is an infinite solution. Approaching the Infinite Solution TopicMaths is a very practical subject. It doesn’t involve any learning and requires a practical bend of mind. Therefore, if one intends to excel in the subject, practice is simply the key to success. The students must approach the subject through its syllabus. The syllabus talks about the topics and how much time one can take to cover every topic. Next comes the previous year question paper. The idea of reading the previous year question paper gives one the competitive edge. These question papers must be practised by the students more than twice. Such a routine of practising the questions will evolve one’s skills as per the requirement of the exams. Self EvaluationSelf-evaluation is a very important component of the examination process. It enables one to judge oneself very clearly and take note of the depth of understanding about a concept. To judge one’s calibre with the infinite solutions topic, a student must give a lot of tests and attempt mock question papers. The performance in these tests and mocks determine the final performance in the examination of the students. Students must record their performance in each test and try to fill the gaps which they can highlight through this mythology. The expert teachers of the subject recommend students not to take this part of preparation lightly and use it actively to judge and enhance one’s performance. The Vedantu EdgeThe infinite solutions topic is prepared by highly experienced teachers of Vedantu who understand the needs of the students and are very much acquainted with the latest trends in the examination. The students stand at a very lucrative spot to take advantage of their knowledge and experience and enhance their performance. The students can use the article above for revisions and as well as keep themselves abreast with the level of competition that one faces today. A student can either underline the keywords or notice only the same every time he/she revisits the content for revision or make revision notes from the same. Since the article is a reflection of the latest trends in the exams and the toughness one has to face in the exams, students can condition themselves for the same when they go through the article. Download Infinite Solutions - Definition, Conditions, and Examples article and get your Vedantu edge now! |
