An equation is written as two expressions, connected by an equals sign ("="). The expressions on the two
The … See more

Two equations or two systems of equations are equivalent, if they have the same set of solutions. The following operations transform an equation or a system of equations into an equivalent one – provided that the op… See more

An equation is analogous to a weighing scale, balance, or seesaw.
Each side of the equation corresponds to one side of the balance. Different quantities can be placed on each side: if the weights on the two … See more

Algebra studies two main families of equations: polynomial equations and, among them, the special case of linear equations. When there is only one variable, polynomial equations have the form P(x) = 0, where P is a … See more

In Euclidean geometry, it is possible to associate a set of coordinates to each point in space, for example by an orthogonal grid. This method allows one to characterize geometric figures by equations. … See more

A Diophantine equation is a polynomial equation in two or more unknowns for which only the integer solutions are sought (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantin… See more

A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the eq… See more