Precisely because of the inequality! Take the simplest case, of an equation or inequality that is already solved. For the equation, for example, take:
x = 10
The equality means that x has to be 10, it can't be anything else. On the other hand, a similar inequality:
x > 10
means that ANY number greater than 10 will do.
For the sake of completeness, please note that more complicated equations can actually have more than one solution, too. For example: x2 = 25 has the solutions 5 and -5, while sin x = 0 has infinitely many solutions, since the sine function is periodic.
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A system of equations can have any number of inequalities.
No, inequalities have more than, less then, at least, or no more than signs. Equations just have equal signs. An inequality answer can't be written as just a number it has to have a sign with it.
In question and answer logic answers are given and if they fall in an area bounded by the inequality then it is a good answer. After graphing three or more inequalities the vertexes are the possible maxima of the system of equations.
It is a set of equations, which is also called a system of equations. There may be no solution, a single (unique) solution or more than one - including infinitely many.
Put the values that you find (as the solution) back into one (or more) of the original equations and evaluate them. If they remain true then the solution checks out. If one equation does not contain all the variables involved in the system, you may have to repeat with another of the original equations.