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.
If an equation simplifies such that the variable cancels out and results in a true statement (like (5 = 5)), it has infinitely many solutions. This is because any value of the variable will satisfy the equation. Conversely, if the simplification leads to a false statement (like (5 = 3)), it has no solutions.
A linear equation in one variable has one solution. An equation of another kind may have none, one, or more - including infinitely many - solutions.
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
-- 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.
Inequalities tend to have infinitely many solutions.
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.
If an equation simplifies such that the variable cancels out and results in a true statement (like (5 = 5)), it has infinitely many solutions. This is because any value of the variable will satisfy the equation. Conversely, if the simplification leads to a false statement (like (5 = 3)), it has no solutions.
A linear equation in one variable has one solution. An equation of another kind may have none, one, or more - including infinitely many - solutions.
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
If the solution contains one variable which has not been fixed then there are infinitely many solution.
Infinitely many
-- 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.
It has infinitely many solutions.
Inequalities tend to have infinitely many solutions.
Is a trigonometric equation which has infinitely many real solutions.
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That means the same as solutions of other types of equations: a number that, when you replace the variable by that number, will make the equation true.Note that many trigonometric equations have infinitely many solutions. This is a result of the trigonometric functions being periodic.