It is an equation with no solutions [in the given domain]. There may (or may not) be solutions if you change the domain.
For example, if X is an integer, then 5X = 2 has no solution. But if you change the domain to rational numbers, then X = 2/5 or 0.4 is a solution.
The idea is that a regular equation is simply a statement that two quantities are the same; this statement may, or may not, be true - or it may depend on the value of the variables. For example, x + 2 = 5 is true, only if x is replaced with 3. An "identity" is an equation that is true for any value of the variables.
x - 1 = x + 1
In the equation x = 3, if x = 3, the equation is true, if x has any other value, it is not. The value of any other variable, such as y, is irrelevant. I would say that the answer is 0 because otherwise y is part of the equation which clearly it isnt.
An ordered pair is a solution only of a linear equation in two variables - not any linear equation. Often the variables are denoted by x and y. If the first of the ordered pair is substituted for x in the equation, and the second for y, then the equation represents a true statement.
It is an identity.
In algebra, variables are represented by letters such as x. A variable could be any number. That number is the "value" of the variable. In an expression, you can choose a number to put in for x, and simplify to get a number which is the value of the expression. In an equation, you can solve for the value of x, which will be the value of x which makes the equation true.
It is true for all permissible values of any variables in the equation. More simply put, it is always true.
Any number that makes an equation true is a 'solution of an equation'. it is a solution
Such a value is said to be a solution, or a root, of the equation.
Such an equation is called an IDENTITY.
An identity is an equation that is always true, for any value of the variable or variables. Here are some examples: x + x = 2x a + b = b + a x1 = x
If an equation has two variables, we'll call them (x,y), the variables can be any value as long as both sides of the equation have the same result. If the equation was x = y, then the variables could be (1,1), (2,2), (3,3),etc...
The idea is that a regular equation is simply a statement that two quantities are the same; this statement may, or may not, be true - or it may depend on the value of the variables. For example, x + 2 = 5 is true, only if x is replaced with 3. An "identity" is an equation that is true for any value of the variables.
linear equation in one variable
"n", as well as other letters, are used as variables. They can contain any value; quite often, you need to find out what value you should replace to make an equation valid. For example, in: n + 1 = 4 In this case, if you replace "n" with "3", the equation will be satisfied (true); for any other value it won't.
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.
x - 1 = x + 1