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.
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.
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
Is a trigonometric equation which has infinitely many real solutions.
The equation has infinitely 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.
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.
Infinitely many
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.
It has infinitely many solutions.
Is a trigonometric equation which has infinitely many real solutions.
The equation has infinitely 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.
There are infinitely many solutions to 11x - 99 = 11(x - 9)
Strictly speaking the above equation is a tautological equation or an IDENTITY. An identity is true for all values of any variables that appear in it. Thus, the above "equation" is true for all value of x. - that is, it has infinitely many solutions.
No, it can be an inequality, such as x+5>2. An inequality usually has (infinitely) many solutions.
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
There are infinitely many solutions to the equation since it simplifies to 13 = 13, which is always true.