system of equations
Imagine two clues about the same pair of mystery numbers: one clue tells you their sum, another tells you their difference. Neither clue alone pins the numbers down, but together they often do. A system of equations is exactly that — a bundle of two or more equations that share the same unknowns, considered all at once rather than one at a time.
Formally, a system is a collection of equations in the same variables, and you seek values of those variables that make every equation true at the same moment. The most common case is two linear equations in two unknowns, like x + y = 5 and x − y = 1, but systems can have any number of equations and unknowns, and the equations need not be linear.
A system is not just a list you solve separately; the whole point is the shared solution. An honest caveat: having two equations does not guarantee exactly one answer. Depending on how the equations relate, a system may have one solution, none at all, or infinitely many — distinctions captured by the words consistent, inconsistent, and dependent.
The system x + y = 5, x − y = 1 has the single solution x = 3, y = 2, since both equations hold for that pair.
Two clues, one shared answer.
A curly brace is often drawn to the left of the stacked equations to signal that they belong to one system. The number of equations and the number of unknowns need not match.