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Calculus

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

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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.

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Related Questions

Explain how to identify whether an equation has no solution or infinitely many solutions?

An equation can be determine to have no solution or infinitely many solutions by using the square rule.

How do you know when an equations has infinitly many solutions?

An equation must have 1, 0, or infinitely many solutions. So if you find 1 and there is another, you have know it has infinitely many. For example. 0x+2=2 I solve this and the equations become 0x=0 Now, 1 is a solutions, but so is 2. I now know there are infinitely many. How about 0x+2=3. No solution and 2x+2=4, has one solution. I put those two here so you might try other numbers and see that they have no solutions and one solution. A special type of equation known as an identity is an equation that holds for all numbers. This means it has infinitely many solutions.

How many solutions does linear equation in two variable have?

A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.

Sec2x equals 3?

Is a trigonometric equation which has infinitely many real solutions.

How do you know when an Equation has an infinity solutions without solving the equation?

You can't really know that in all cases. But with some practice in working with equations, you'll start to notice certain patterns. For example, you'll know that certain functions are periodic, and that an equation such as: sin(x) = 0 have infinitely many solutions, due to the periodicity of the function. This one is easy; we can make some small changes: sin(2x + 3) = 0.5 Here it isn't as easy to guess the exact solutions of the equation, but due to our knowledge of the periodicity of the sine function, we can assume that it has infinitely many solutions. Another example: a single equation with two or more variables normally has infinitely many solutions, for example: y = 3x + 2

When you solve equation describe how you know when there will be a infinite solutions?

If the solution contains one variable which has not been fixed then there are infinitely many solution.

What is the solution of 4y minus x equals 10?

The equation has infinitely many solutions.

Which best explains why the equation 7x plus 3 equals 7x plus 3 has infinitely many solutions?

Strictly speaking the above equation is a tautological equation or an IDENTITY. An identity is true for all values of any variables that appear in it. Thus, the above "equation" is true for all value of x. - that is, it has infinitely many solutions.

What are inifintly equations?

Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.

Does an open sentence have to be an equation?

No, it can be an inequality, such as x+5&gt;2. An inequality usually has (infinitely) many solutions.

How do you know when a equation has an infinte number of solutions?

-- A single equation with more than one variable in it has infinitely many solutions. -- An equation where the variable drops out has infinitely many solutions. Like for example x2 + 4x -3 = 0.5 (2x2 + 8x - 6) As mean and ugly as that thing appears at first, you only have to massage it around for a few seconds to get -3 = -3 and that's true no matter what 'x' is. So any value for 'x' is a solution to the equation, which means there are an infinite number of them.

An equation has one solution?

A linear equation in one variable has one solution. An equation of another kind may have none, one, or more - including infinitely many - solutions.

When you use the substitution method how can you tell that a has an infinite number of solutions?

If the process of substituting leads to an identity rather than an equation then the system has infinitely many solutions.

What 3D shapes has a one square base?

There are infinitely many possible solutions. The question needs to be more specific.There are infinitely many possible solutions. The question needs to be more specific.There are infinitely many possible solutions. The question needs to be more specific.There are infinitely many possible solutions. The question needs to be more specific.

Can linear system that has more unknowns than equation be consistent?

yes it can . the system may have infinitely many solutions.

How can you tell when an equation in one variable has infinitely many solutions or no solutions?

There is no simple method. The answer depends partly on the variable's domain. For example, 2x = 3 has no solution is x must be an integer, or y^2 = -9 has no solution if y must be a real number but if it can be a complex number, it has 2 solutions.

How do you know when an equation has infinitely many solutions or no solution?

They Are infinitely many solutions for an equation when after solving the equation for a variable(let us suppose x),we get the expression 0 = 0. Or Simply L.H.S = R.H.S For Ex. x+3=3+x x can have any value positive or negative, rational or irrational, it doesn't matter the sequence will be infinite. And No Solutions when after solving the equations the expression obtained is unequal For Ex. x+3=x+5 for every value of x, The Value in L.H.S And R.H.S. will differ. Hence It Has No Solutions.

What must be true about the lines of a system of equation that has not one solution but infinitely many solutions?

There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.

How many solutions are there to the equation below 11x - 99 11(x - 9)?

There are infinitely many solutions to 11x - 99 = 11(x - 9)

How do you identify 2 solutions to a linear equation?

A linear equation is that of a straight line. Any one of the infinitely many points on the line will be solutions. If the equation is in terms of the variables x and y, just pick any two values of x, solve for y and the results will be the coordinates of two solutions.

How do you know how many solutions a quadratic equation will have?

A quadratic equation has the formAx2 + Bx + C = 0,where A, B, and C are numbers and x is a variable. Since the polynomial here has degree 2 (the highest exponent of x), it either has 0, 1, 2, or infinitely many solutions.The infinitely many solutions only happens when A, B, and C are all equal to zero. Otherwise, we can find the number of solutions by examining the discriminant, which in this case is the quantity B2 - 4AC. If the discriminant is negative, there are no (real) solutions. If the discriminant equals zero, we have what is called a "repeated root" and there is exactly one (real) solution. Otherwise, if the discriminant is positive, there are two distinct (real) solutions.

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