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In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality. A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set.
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]
The solution set for the equations = and + = is the single point (2, 3). An example of solving a system of linear equations is by using the elimination method: {+ = = Multiplying the terms in the second equation by 2:
Each free variable gives the solution space one degree of freedom, the number of which is equal to the dimension of the solution set. For example, the solution set for the above equation is a line, since a point in the solution set can be chosen by specifying the value of the parameter z. An infinite solution of higher order may describe a ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
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