What characterizes a linear system of equations?

A linear system of equations is characterized by multiple linear equations that involve shared variables, all of which aim to find simultaneous solutions. The key aspect of linear systems is that each equation represents a linear relationship among the variables; this means that each one can be expressed in the form of a straight line when graphed in two dimensions. The equations do not have terms that involve products of variables, powers greater than one, or any nonlinear functions.

In seeking simultaneous solutions, the goal is typically to find values for the variables that satisfy all equations in the system at the same time. This leads to one or more solution sets that can be interpreted graphically as the points of intersection of the lines represented by the equations.

In contrast, the other options deviate from this fundamental concept by either implying nonlinearity, introducing quadratic terms, or suggesting a scenario with multiple outputs without the clarity or definitions that accompany a linear relationship. Each of those other explanations reflects scenarios that do not align with the standard definition of a linear system of equations.