In the simplest case, it will be a number. But you can also set up equations which you are supposed to solve for ONE of the variables - in which case the solution may involve OTHER variables.
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The solution may be either. The solution of a differential equation, for example, may contain an unknown (variable) constant of integration.
The number that replaces a variable is the solution to the equation. great question, but it's only the answer.??
When you put the number in place of the variable (like maybe the 'x' or the 'y') wherever the variable occurs in the equation, and the statement you get out of all the numbers you have is not true, then you know the number is not a solution.
Answer 1 == In an open sentence (an equation or inequality with a variable in it), when a number replacing the variable makes the sentence true, then it is a solution.
-- If the equation has only one variable (like 'x' or 'y'), and the only power of the variable anywhere in the equation is '1', then the equation has one solution. -- If the variable appears raised to powers higher than '1', then there are as many solutions as the highest power of the variable. -- If the equation has two or more variables, then there are an infinite number of solutions.
undefined means you can not do the operation (5/0 is undefined) no solution refers to an equation not having an answer. a solution is a number which you can plug into the variable of an equation and get a true statement. So having no solution means there is no number which you can plug in and get a true statement. As a fraction is not an equation, but an expression it is not right to say that 5/0 has no solution. There is no variable in 5/0, nothing to plug into to get a true or false statement.