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There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:
Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.
If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.
There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:
Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.
If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.
There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:
Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.
If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.
There are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:
Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.
If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.
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SteveThere are many different kinds of equations, and each kind requires special techniques for solving; so it probably isn't possible to give rules that are valid in all cases. In any case, here are some specific examples; I am sure there are others which I don't remember right now:
Trigonometric equations quite often have an infinite number of solutions, because they are periodic. To give a simple example, sin x = 0 has the solution x = 0, but also pi, 2xpi, 3xpi, etc. (equivalent to 180 degrees, 360 degrees, etc.), because of the periodic nature of the sine function.
If a variable disappears when solving an equation, if you get a true statement the solution set is the set of all real numbers. For example, 2(x+1) = 2x + 2. Solving, you get: 2x + 2 = 2x + 2, or 0 = 0. Note that the variable "x" disappeared.
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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.
Sec2x equals 3?
Is a trigonometric equation which has infinitely many real solutions.
What is the solution of 4y minus x equals 10?
The equation has infinitely many solutions.
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.
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.
