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How do you recognize when an equation has no real solution or an infinite number of solutions?
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions.
A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions.
Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite.
A function defined as follows:
f(x) = 1 if x is real
f(x) = 0 if x is not real
has no real solutions but an infinite number of solutions in complex numbers.
What else can I help you with?
How many solutions does the equation have?
The number of solutions an equation has depends on the nature of the equation. A linear equation typically has one solution, a quadratic equation can have two solutions, and a cubic equation can have three solutions. However, equations can also have no solution or an infinite number of solutions depending on the specific values and relationships within the equation. It is important to analyze the equation and its characteristics to determine the number of solutions accurately.
What types of solutions can be found for linear equation?
A linear equation has a n infinite number of solutions. The coordinates of each point on the line is a solution.
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 type of system equation produces the solution set infinite solution?
If the equations of the system are dependent equations, which represent the same line; therefore, every point on the line of a dependent equation represents a solution. Since there are an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 3x + 2y = 8 6x + 4y = 16
If a system has an infinite number of solutions does it follow that any ordered pair is a solution?
No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.
What is an infinite solution to an equation?
An infinite solution means that are an infinite number of values that are solutions.
How many solutions does the equation have?
The number of solutions an equation has depends on the nature of the equation. A linear equation typically has one solution, a quadratic equation can have two solutions, and a cubic equation can have three solutions. However, equations can also have no solution or an infinite number of solutions depending on the specific values and relationships within the equation. It is important to analyze the equation and its characteristics to determine the number of solutions accurately.
Does an equation has a solution?
Yes and sometimes it can have more than one solution.
Does this system of equation 5x - y equals 7 have one solution no solution or an infinite number of solutions?
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What is an infinite solution?
The equation or a system of equations having infinite solutions is called identity/identities. (a+b)^2=a^2+2ab+b^2 is an identity. It has infinite solutions. The equation is true for all values of a and b.
What types of solutions can be found for linear equation?
A linear equation has a n infinite number of solutions. The coordinates of each point on the line is a solution.
Is it possible for an equation to have many solutions and can an equation have no solutions?
Yes and yes. eg x = y + 1 has an infinite number of solutions, and {sin(x) + cos(x) = 2} does not have a solution.
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.
Can a pair of linear equation have exactly two solutions?
No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).
What does one solution mean in math?
An equation may have zero, one, or more solutions (this is also true for a system of equations). The equation 2 + x = 5 has only solution, for example. x can only equal 3, so there is one solution. (An example of an equation with more that one solution is x2 = 4. In this case x can equal 2 or -2, so this equation has two solutions. An example of an equation with an infinite number of solutions is x + 6 = 3*2 + x. x can equal any number to make this equation true, so it has an infinite number of solutions. The equation x = x + 1 is an example of an equation with no solutions.)
Is there an explicit solution to a single linear equation with two variables?
Such an equation has an infinite set of solutions. You can solve the equation for one variable, in terms of the other. Then, by replacing different values for one of the variables, you can get different solutions.
What has an infinite number of solutions?
A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.
