systems of equations

A system of equations involves two or more equations that must be solved simultaneously. For a unique solution to exist, the number of equations typically needs to match the number of unknowns. If a solution is found, the system is considered consistent; otherwise, it's inconsistent.1

Linear equations, a fundamental type, express a first-degree polynomial's equality to a constant. For instance, ax + by = c is a linear equation in two variables, representing a straight line in Cartesian coordinates. When multiple linear equations are considered together, they form a system of simultaneous equations. Solving these systems can be done through substitution for simpler cases, but larger systems are more efficiently handled using matrix techniques. Equations are central to mathematics and are used to express many laws of physics.213