Equation solving

Equation solving is the process of finding values of unknowns that make an equation true. Its solutions form the equation’s solution set.

Equivalent equations: Equations are equivalent when they have exactly the same solutions. Valid transformations preserve solutions by replacing an equation with an equivalent one.
Equation: A mathematical statement asserting that two expressions have equal values. Solving works on equations by identifying values that make the equality true.
Word problem: A problem stated in ordinary language that can be represented mathematically. Modeling translates described quantities and constraints into equations to solve.
Numerical analysis: The study of algorithms that approximate mathematical quantities and solutions with finite computation. Numerical methods return approximations when exact solutions are unavailable or costly.
Inverse operation: An inverse operation undoes another operation, such as subtraction undoing addition. Inverse operations isolate an unknown while preserving equality.
Variable: A symbol that represents a quantity whose value may be unknown or change. Variables mark the quantities whose possible values solving seeks.
Inverse problem: A problem that infers causes or parameters from observed effects or measurements. Many inverse problems reduce to finding unknowns that satisfy equations linking data and parameters.
Symbolic computation: Computer manipulation of mathematical expressions in exact symbolic form. Symbolic solvers seek exact expressions rather than only numerical values.
Substitution method: A method for solving a system by replacing one variable with an equivalent expression. Substitution reduces a system to an equation in fewer variables.
Equality: A relation stating that two mathematical expressions have the same value. Maintaining equality is the basis for valid algebraic transformations.

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