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-- 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.
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How do you know when an equation has an infinite amount of solutions?
If the equation is an identity.
How do you know if a quadratic equation will have whether or not it will have solutions?
Factorise it!
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 if a series converges by the intergral test?
When you take the integral using the series as integrand, it converges if the integral worked out to be a number. If it's infinte, the series diverge.
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
