What is a system of equations?

A system of equations consists of two or more equations that share the same set of variables. This commonality allows for the exploration of relationships between those variables, often enabling the determination of their values that satisfy all equations in the system simultaneously. Solving a system can involve finding points of intersection on a graph or identifying values that make all equations true at the same time.

In contrast, a set of equations having different variables does not fit the definition of a system of equations because the solutions to each equation pertain to different entities rather than an interconnected system. A single equation with multiple solutions describes a scenario where one equation can yield various outcomes, but it doesn't encompass the idea of multiple equations working together. Lastly, an equation that contains inequalities involves a different concept; inequalities express a range of possible values and do not focus on finding simultaneous solutions as in a system of equations. Thus, the idea of a system specifically revolves around interrelated equations sharing common variables, making the correct choice the one that highlights this relationship.