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How do you know when an equation has infinitely many solutions or no solution?
Wiki User
∙ 14y ago
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.
Wiki User
∙ 14y ago
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Why do we represent the solution to an inequality with a graph on a number line but we don't do the same for the solution to an equation?
An equation has an equal sign, which means that we know what the variable is equal to :)
Why do you isolate the variable on one side the the equation when solving a linear equation?
Isolating a single variable in terms of the rest of the equation provides a solution to that variable. That is, if you know the equation that equals the variable, then you can figure out its value.
How do you identify solutions to equations?
You'll know that you've found the equation's solutions when you end up with an expression in the form of x=N. Where x is what you're trying to find solutions to and N is either a number or an expression not dependent on x.
What is an equation that has no solution is called and 8203?
It is called an equation with no solutions in the domain under consideration. It is quite possible that an equation which does not have a solution in one domain has a simple solution in another - possibly broader - domain.For example,a junior school pupil may tell you that x + 3 = 2 has no solution. In the domain of positive integers it does not but perhaps a year later, they will tell you that the answer is x = -1.a little later they may tell you that 3*x = 2 has no solution in the domain of integers. True, but in the domain of rational numbers, the answer is x = 2/3.Next, x2 = 2 has no solution in rational numbers but x = sqrt(2), is a perfectly valid solution in the domain of real numbers (which includes irrational numbers).Still further, x2 = -9 has no solution in real numbers since we all know that 32 = +9 and (-3)2 = +9. However, in the domain of imaginary numbers, x = 3i.and so on.Also, there are equations which cannot be solved analytically, but do have solutions which can be found by numerical methods.
How do you know if a quadratic equation can be factored?
The answer depends on what the factors will be. For example, every quadratic can be factored if you allow complex numbers. If not, then it helps to use the discriminant. If it is positive, there are two real factors or solutions. If that positive number is a perfect square, then the factors are rational numbers. If not, they are real but not rational (irrational). If the discriminant is 0, there is one real solution. Lastly, if it is negative, there are no real solutions.
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.
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 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 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.
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
How do you know if a quadratic equation will have one two or no solutions How do you find a quadratic equation if you are only given the solution Is it possible to have different quadratic equation?
Draw the graph of the equation. the solution is/are the points where the line cuts the x(horisontal) axis .
How do you find the linear system if you know its solutions?
You cannot since there are infinitely many sets of lines that can pass through any single point - the solution.
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.
How do you know when an algebraic equation has infinitely many solutions?
A system of equations has an infinite set of solutions when the equations define the same line, such that for ax + by = c, the values for two equations is a1/a2 + b1/b2 = c1/c2. Equations where a variable drops out completely, e.g. 3x - y = 6x -2y there are either an infinite number of solutions, or no solution at all.
How many solutions are there to the equation x2-48 equals 0?
Quadratic equations like this one usually have two solution. Sometimes they have one (so-called "double") solution. If you solve it, you'll know for sure.
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.
How would you know that your equation has infinite solutions without actually solving it?
In some cases, a knowledge of the function in question helps. For example, when you have multiple equations, if you have more equations than variables you will usually have infinite solutions. Another example is that certain functions are known to be periodic, for instance the trigonometric functions - so an equation such as sin(x) = 1/2 may have infinite solution, due to the periodicity.
