All values of a variable that satisfies equality, inequality, system of equations, or system of inequalities can be termed as solution set. All the values that are in a set for whom any equation is satisfied can be interpreted with the help of any feasible solution may it be graphical or algebraic. Solution of any equation or in equation depends upon the domain of the subject and its availability.
For example if we assume a linear equation as 3x + 2y = 12, then we need to find all the values of x and y that satisfied the given equation. All the values of x and y that satisfies the above equation can be put under one definite set, such as one set would be (2,3), similar to this there can be many sets of solution available.
Let us take another example as 5x + 6y = 30. Then one of the solution set of an equation would be (6,0). Now it is true that there may be many solution-sets and when we integrate all of them together we call it as a set.
There are many different ways to solve an equation, out of which most popular is solving it by hit and trial method. The other most prominent is the matrix solution by substitution the coefficient values of the equation. Any solution set of an equation depends on the type of variable it is having.
While dealing with algebra we will come across many such equations having unique solution and having infinite solutions.
Moreover solution set examples could be found in the questions of probabilities and permutations and combinations. Algebra is that part of mathematics that deals more about numbers in the form of equations. Apart from the linear equations there more complex equations for which solution-set can be determined, more complex the equation is, and more complex is the solution-set. For linear equations there may be more than one variable, but most important is that the degree of the equation should be one.
Similarly we have quadratic equations whose degree is two, means we get two solutions for one variable each time we solve. More preciously the solution-set may consist of degenerated sets, which might be imaginary numbers, but still can provide the solution.
So hence all equations have some solutions unique, some or infinite, which together collected and can be names as solution set.