solves

Solves is the third-person singular present tense of the verb solve. It denotes the act of finding a solution to a problem, puzzle, equation, or mystery. The verb solve comes from Latin solvēre, meaning to loosen or untie, and entered English through Old French solver, acquiring the sense of resolving a difficulty over time.

In mathematics and related fields, the phrase "the equation solves" or "the method solves for x" describes determining the value or values of a variable that satisfy the given conditions. A single equation may have zero, one, or multiple solutions. In linear algebra, solving a system means finding a set of values that satisfy all equations simultaneously. In optimization, a solver seeks a feasible or optimal solution.

In computing, solvers are programs or libraries that compute solutions to problems posed in a formal language, such as linear programming solvers, polynomial equation solvers, or SAT solvers. The statement "the program solves the problem" indicates that a valid result has been found, though some problems are undecidable or intractable within practical limits.

In everyday language, "solves" is used to describe overcoming challenges: "She solves crosswords quickly." The noun form "solution" refers to the answer itself; "solvability" describes whether a problem can be solved. The term appears across disciplines, reflecting the common aim of identifying a correct or best possible resolution to a given question or constraint.