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The solution set of a given set of equations or inequalities is the set of all its solutions, a solution being a tuple of values, one for each unknown, that satisfies all the equations or inequalities. If the solution set is empty, then there are no values of the unknowns that satisfy simultaneously all equations and inequalities.
The set of solutions of a real linear inequality constitutes a half-space of the 'n'-dimensional real space, one of the two defined by the corresponding linear equation. The set of solutions of a system of linear inequalities corresponds to the intersection of the half-spaces defined by individual inequalities.
In mathematics, the solution set of a system of equations or inequality is the set of all its solutions, that is the values that satisfy all equations and inequalities. [1] Also, the solution set or the truth set of a statement or a predicate is the set of all values that satisfy it. If there is no solution, the solution set is the empty set. [2]
Solution set (portrayed as feasible region) for a sample list of inequations. Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an inequation or a conjunction of several inequations.
The values of the variables which make the equation true are the solutions of the equation and can be found through equation solving. Another type of equation is inequality. Inequalities are used to show that one side of the equation is greater, or less, than the other.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a , b , c , and d of the cubic equation are real numbers , then it has at least one real root (this is true for all odd-degree polynomial functions ).
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